Hypothesis Generation
spacering-net/codeg
Structured hypothesis formulation from observations. An agent skill from spacering-net/codeg.
Problem-solving strategies for banach spaces in functional analysis
Install Banach Spaces
$ npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install parcadei/Continuous-Claude-v3 banach-spaces --agent claude-codeProject scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/functional-analysis/banach-spaces .claude/skills/banach-spaces && rm -rf skills-srcUse ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.
Claude Code skills documentation · loads skills from .claude/skills/
Install the "banach-spaces" agent skill from https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spaces into .claude/skills/banach-spaces/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "banach-spaces", then confirm the skill loads.Claude Code copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$skill-installer install https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spacesType this inside Codex. $skill-installer <name> installs a curated skill from openai/skills. The installer writes to $CODEX_HOME/skills (default ~/.codex/skills). Restart Codex if the skill does not show up.
$ npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install parcadei/Continuous-Claude-v3 banach-spaces --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .agents/skills && cp -r skills-src/.claude/skills/math/functional-analysis/banach-spaces .agents/skills/banach-spaces && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "banach-spaces" agent skill from https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spaces into .agents/skills/banach-spaces/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "banach-spaces", then confirm the skill loads.Codex copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install parcadei/Continuous-Claude-v3 banach-spaces --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/.claude/skills/math/functional-analysis/banach-spaces .cursor/skills/banach-spaces && rm -rf skills-srcUse ~/.cursor/skills/ instead of .cursor/skills for a personal install.
Cursor skills documentation · loads skills from .cursor/skills/, .agents/skills/, .claude/skills/, .codex/skills/
Install the "banach-spaces" agent skill from https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spaces into .cursor/skills/banach-spaces/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "banach-spaces", then confirm the skill loads.Cursor copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gemini skills install https://github.com/parcadei/Continuous-Claude-v3.git --path .claude/skills/math/functional-analysis/banach-spaces--scope user (default) or --scope workspace; --path is the subfolder of the repo that holds the skill; --consent skips the security confirmation prompt.
$ npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install parcadei/Continuous-Claude-v3 banach-spaces --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/.claude/skills/math/functional-analysis/banach-spaces .gemini/skills/banach-spaces && rm -rf skills-srcUse ~/.gemini/skills/ instead of .gemini/skills for a personal install, then run /skills reload.
Gemini CLI skills documentation · loads skills from .gemini/skills/, .agents/skills/
Install the "banach-spaces" agent skill from https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spaces into .gemini/skills/banach-spaces/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "banach-spaces", then confirm the skill loads.Gemini CLI copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gh skill install parcadei/Continuous-Claude-v3 banach-spacesInstalls for Copilot at project scope by default; add --scope user for a personal install. Preview a skill first with gh skill preview. Needs GitHub CLI 2.90.0 or later (public preview).
$ npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .github/skills && cp -r skills-src/.claude/skills/math/functional-analysis/banach-spaces .github/skills/banach-spaces && rm -rf skills-srcUse ~/.copilot/skills/ instead of .github/skills for a personal install. Commit .github/skills so cloud agent and code review can use it.
GitHub Copilot skills documentation · loads skills from .github/skills/, .claude/skills/, .agents/skills/
Install the "banach-spaces" agent skill from https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spaces into .github/skills/banach-spaces/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "banach-spaces", then confirm the skill loads.GitHub Copilot copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install parcadei/Continuous-Claude-v3 banach-spaces --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/.claude/skills/math/functional-analysis/banach-spaces .opencode/skills/banach-spaces && rm -rf skills-srcUse ~/.config/opencode/skills/ instead of .opencode/skills for a personal install.
OpenCode skills documentation · loads skills from .opencode/skills/, .claude/skills/, .agents/skills/
Install the "banach-spaces" agent skill from https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/functional-analysis/banach-spaces into .opencode/skills/banach-spaces/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "banach-spaces", then confirm the skill loads.OpenCode copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
Facts
- Skill name
banach-spaces- GitHub stars
- 3.9k
- Used in
- 1 other repo
- Token cost
- ~889 tokens
- SKILL.md length
- 439 words
- Files
- 1
- Skills in repo
- 141
- Repo updated
- First seen
- Licence
- MIT
At a glance
Problem-solving strategies for banach spaces in functional analysis
- Works in 5 steps: Verify Banach space → Hahn-Banach Theorem → Open Mapping Theorem → …
- Research & Science work in your project
- SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
- Calls uv
What it does
Banach Spaces is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for banach spaces in functional analysis
Its SKILL.md is about 890 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.
It sits in Research & Science. The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.
When your agent uses it
- Research & Science work in your project
Example prompts
- “/banach-spaces”
Requirements
- Python 3
- Pre-approved tools (allowed-tools): Bash, Read
Workflow steps
5 steps, taken from the first numbered list in SKILL.md.
- Verify Banach space
- Hahn-Banach Theorem
- Open Mapping Theorem
- Closed Graph Theorem
- Uniform Boundedness Principle
What it can do on your machine
Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.
Tool permissions
Pre-approves these tools, so the agent can use them without asking each time:
BashRead
From allowed-tools in the SKILL.md frontmatter.
Runs code
Shell commands in SKILL.md call:
uv
From the folder's file list and the shell code blocks in SKILL.md.
Network
No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.
From URLs in SKILL.md, links to its own repository left out.
Credentials
Names no API keys, tokens, secrets or passwords.
From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.
Context cost
Banach Spaces loads about 889 tokens when it runs. Until then it costs about 20 tokens; SKILL.md has 439 words of instructions outside code blocks.
Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.
Safety
Auto-check: notes
The automated check noted patterns worth knowing about, such as sudo or a known installer.
- NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
allowed-tools: Bash, Read
Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.
SKILL.md
The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 439 words, ~889 tokens.
Download SKILL.mdSave it as
.claude/skills/banach-spaces/SKILL.md (or your agent's skills folder).- name
- banach-spaces
- description
- Problem-solving strategies for banach spaces in functional analysis
- allowed-tools
- Bash, Read
Banach Spaces
When to Use
Use this skill when working on banach-spaces problems in functional analysis.
Decision Tree
Verify Banach space
- Complete normed vector space
- Check: every Cauchy sequence converges
z3_solve.py prove "completeness"
Hahn-Banach Theorem
- Extend bounded linear functionals
- Separate convex sets
z3_solve.py prove "extension_exists"
Open Mapping Theorem
- Surjective bounded operator between Banach spaces is open
- Consequence: bounded inverse exists
z3_solve.py prove "open_mapping"
Closed Graph Theorem
- T: X -> Y has closed graph implies T bounded
- Strategy: verify graph closure, conclude boundedness
z3_solve.py prove "closed_graph_implies_bounded"
Uniform Boundedness Principle
- Pointwise bounded family of operators is uniformly bounded
- Application: prove operator families are bounded
Tool Commands
Z3_Completeness
uv run python -m runtime.harness scripts/z3_solve.py prove "cauchy_sequence implies convergent"Z3_Open_Mapping
uv run python -m runtime.harness scripts/z3_solve.py prove "T_surjective_bounded implies T_open"Z3_Closed_Graph
uv run python -m runtime.harness scripts/z3_solve.py prove "graph_closed implies T_bounded"Sympy_Norm
uv run python -m runtime.harness scripts/sympy_compute.py simplify "norm(alpha*x + beta*y)"Key Techniques
From indexed textbooks:
- [Introductory Functional Analysis with Applications] If (X, d) is a pseudometric space, we call a set B(xo; r) = {x E X I d(x, xo) < r} an open ball in X with center Xo and radius r. Note that this is analogous to 1. What are open balls of radius 1 in Prob.
- [Measure, Integration Real Analysis (... (Z-Library)] Section 5C Lebesgue Integration on Rn 11 Suppose E is a subset of Rm Rn and Rm : (x, y) x E for some y . Dene f : R2 R by = (0, 0), (a) Prove that D1(D2 f ) and D2(D1 f ) exist everywhere on R2. Show that D1(D2 f ) (c) Explain why (b) does not violate 5.
- [Real Analysis (Halsey L. Royden, Patr... (Z-Library)] The Hahn-Banach Theorem has a rather humble nature. The only mathematical con- cepts needed for its statement are linear spaces and linear, subadditive, and positively homogeneous functionals. Besides Zorn’s Lemma, its proof relies on nothing more than the rudimentary properties of the real numbers.
- [Introductory Functional Analysis with Applications] If in a normed space X, absolute convergence of any series always implies convergence of that series, show that X is complete. Show that in a Banach space, an absolutely convergent series is convergent. Schauder basis) Show that if a normed space has a Schauder basis, it is separable.
- [Introductory Functional Analysis with Applications] What are the adjoints of a zero operator 0 and an identity operator I? Annihllator) Let X and Y be normed spaces, T: X - Y a bounded linear operator and -M = (¥t( T), the closure of the range of T. Fundamental Theorems for Normed and Banach Spaces To complete this discussion, we should also list some of the main differences between the adjoint operator T X of T: X ~ Y and the Hilbert-adjoint operator T* of T: Hi ~ H 2 , where X, Yare normed spaces and Hi> H2 are Hilbert spaces.
Show full SKILL.md (9 more words)Show less
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file
Files
Just SKILL.md in .claude/skills/math/functional-analysis/banach-spaces of parcadei/Continuous-Claude-v3.
Open the folder on GitHubat commit d07ff4b
Used in 1 other repository
We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.
Compare with similar skills
Banach Spaces next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.
| Skill | Stars | Used in | Tokens | Auto-check | Licence | Repo updated |
|---|---|---|---|---|---|---|
| Banach Spaces this skillparcadei/Continuous-Claude-v3 | 3.9k | 1 repos | ~889 | Automated safety check: Notes | MIT | |
| Hypothesis Generationspacering-net/codeg | 3.9k | 14 repos | ~3.6k | Automated safety check: Notes | MIT | |
| GitHub Deep Researchbytedance/deer-flow | 84k | 4 repos | ~1.3k | Automated safety check: Pass | MIT | |
| Nature Paper CardYuan1z0825/nature-skills | 47k | 2 repos | ~2.1k | Automated safety check: Pass | Apache-2.0 | |
| Content Research Writerweapp-tailwindcss/weapp-tailwindcss | 1.9k | 25 repos | ~3.5k | Automated safety check: Pass | MIT | |
| Last30daysmvanhorn/last30days-skill | 64k | — | ~7.9k | Automated safety check: Notes | MIT |
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Content Research Writer
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Related
Categories
Questions about Banach Spaces
What does Banach Spaces do?
Problem-solving strategies for banach spaces in functional analysis. Banach Spaces is an agent skill from parcadei/Continuous-Claude-v3.
When should I use Banach Spaces?
Banach Spaces fits situations like: research & Science work in your project.
How do I install Banach Spaces in Claude Code?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a claude-code`. Or copy the skill folder (.claude/skills/math/functional-analysis/banach-spaces in parcadei/Continuous-Claude-v3) into .claude/skills/banach-spaces in your project. Claude Code loads it when a task matches its description.
How do I install Banach Spaces in Codex?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a codex`. Or copy the skill folder (.claude/skills/math/functional-analysis/banach-spaces in parcadei/Continuous-Claude-v3) into .agents/skills/banach-spaces in your project. Codex loads it when a task matches its description.
Can I use Banach Spaces in Cursor, Gemini CLI or GitHub Copilot?
Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/banach-spaces, .gemini/skills/banach-spaces, .github/skills/banach-spaces and .opencode/skills/banach-spaces in your project.
What does Banach Spaces need to run?
Going by SKILL.md and its folder, Banach Spaces needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.
Does Banach Spaces access the network?
SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.
Is Banach Spaces safe to install?
Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.
What licence does Banach Spaces use?
Banach Spaces is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.
How many tokens does Banach Spaces use?
About 889 tokens (SKILL.md is roughly 3.6k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.
What are the alternatives to Banach Spaces?
Skills that share tags, products or a category with Banach Spaces: Hypothesis Generation (spacering-net/codeg, 3.9k stars), GitHub Deep Research (bytedance/deer-flow, 84k stars), Nature Paper Card (Yuan1z0825/nature-skills, 47k stars) and Content Research Writer (weapp-tailwindcss/weapp-tailwindcss, 1.9k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
Who maintains Banach Spaces?
parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,943 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.
Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.