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Agent skill

Compactness

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for compactness in topology. An agent skill from parcadei/Continuous-Claude-v3.

MITAuto-check: notesResearch & Science

Install Compactness

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill compactness -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 compactness --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ 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/topology/compactness .claude/skills/compactness && rm -rf skills-src

Use ~/.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/

Facts

Skill name
compactness
GitHub stars
3.9k
Used in
1 other repo
Token cost
~732 tokens
SKILL.md length
254 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for compactness in topology. An agent skill from parcadei/Continuous-Claude-v3.

  • Works in 4 steps: Is X compact? → Compactness Tests → Product Spaces → …
  • Tasks that involve Math and symbolic computation
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Compactness is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for compactness in topology

Its SKILL.md is about 730 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, covering Math and symbolic computation. It works with SymPy. 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

  • Tasks that involve Math and symbolic computation

Example prompts

  • “/compactness”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

4 steps, taken from the first numbered list in SKILL.md.

  1. Is X compact?
  2. Compactness Tests
  3. Product Spaces
  4. Consequences of Compactness

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:

    • Bash
    • Read

    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

Compactness loads about 732 tokens when it runs. Until then it costs about 17 tokens; SKILL.md has 254 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~17
When it runs · the whole SKILL.md, loaded when a task matches
~732

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). 254 words, ~732 tokens.

Download SKILL.mdSave it as .claude/skills/compactness/SKILL.md (or your agent's skills folder).
name
compactness
description
Problem-solving strategies for compactness in topology
allowed-tools
Bash, Read

Compactness

When to Use

Use this skill when working on compactness problems in topology.

Decision Tree

  1. Is X compact?

    • If X subset R^n: Is X closed AND bounded? (Heine-Borel)
    • If X is metric: Does every sequence have convergent subsequence?
    • General: Does every open cover have finite subcover?
    • z3_solve.py prove "bounded_and_closed"

  2. Compactness Tests

    • Heine-Borel (R^n): closed + bounded = compact
    • Sequential: every sequence has convergent subsequence
    • sympy_compute.py limit "a_n" --var n to check convergence

  3. Product Spaces

    • Tychonoff: product of compact spaces is compact
    • Finite products preserve compactness directly

  4. Consequences of Compactness

    • Continuous image of compact is compact
    • Continuous real function on compact attains max/min
    • sympy_compute.py maximum "f(x)" --var x --domain "[a,b]"

Tool Commands

Z3_Bounded_Closed
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "bounded_and_closed"
Sympy_Limit
bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo
Sympy_Maximum
bash
uv run python -m runtime.harness scripts/sympy_compute.py maximum "f(x)" --var x --domain "[a,b]"

Key Techniques

From indexed textbooks:

  • [Topology (Munkres, James Raymond) (Z-Library)] CompactSpaces163 164ConnectednessandCompactnessCh. Itisnotasnaturalorintuitiveastheformer;somefamiliaritywithitisneededbeforeitsusefulnessbecomesapparent. AcollectionAofsubsetsofaspaceXissaidtocoverX,ortobeacoveringofX,iftheunionoftheelementsofAisequaltoX.
  • [Real Analysis (Halsey L. Royden, Patr... (Z-Library)] If X contains more than one point, show that the only possible extreme points of B have norm 1. If X = Lp[a, b], 1 < p < ∞, show that every unit vector in B is an extreme point of B. If X = L∞[a, b], show that the extreme points of B are those functions f ∈ B such that |f | = 1 almost everywhere on [a, b].
  • [Topology (Munkres, James Raymond) (Z-Library)] ShowthatinthenitecomplementtopologyonR,everysubspaceiscom-pact. IfRhasthetopologyconsistingofallsetsAsuchthatR−AiseithercountableorallofR,is[0,1]acompactsubspace? ShowthataniteunionofcompactsubspacesofXiscompact.
  • [Real Analysis (Halsey L. Royden, Patr... (Z-Library)] The Eberlein-ˇSmulian Theorem . Metrizability of Weak Topologies . X is reexive; (ii) B is weakly compact; (iii) B is weakly sequentially compact.
  • [Topology (Munkres, James Raymond) (Z-Library)] SupposethatYiscompactandA={Aα}α∈JisacoveringofYbysetsopeninX. Thenthecollection{Aα∩Y|α∈J}isacoveringofYbysetsopeninY;henceanitesubcollection{Aα1∩Y,. Aαn}isasubcollectionofAthatcoversY.

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/topology/compactness 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

Compactness 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.

Compactness compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Compactness this skillparcadei/Continuous-Claude-v33.9k1 repos~732Automated safety check: NotesMIT
SympyzLanqing/codex-claude-academic-skills4.6k16 repos~3.4kAutomated safety check: PassMIT
Edu Analytic Geometrywy51ai/edulab1.4k1 repos~1.6kAutomated safety check: PassApache-2.0
Edu Solid Geometrywy51ai/edulab1.4k1 repos~1.1kAutomated safety check: PassApache-2.0
Math Toolsananddtyagi/cc-marketplace6872 repos~1.3kAutomated safety check: PassNone
Edu Chem Reactionwy51ai/edulab1.4k—~1.2kAutomated safety check: PassApache-2.0

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Works with

Categories

Questions about Compactness

What does Compactness do?

Problem-solving strategies for compactness in topology. An agent skill from parcadei/Continuous-Claude-v3. Compactness is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Compactness?

Compactness fits situations like: tasks that involve Math and symbolic computation.

How do I install Compactness in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill compactness -a claude-code`. Or copy the skill folder (.claude/skills/math/topology/compactness in parcadei/Continuous-Claude-v3) into .claude/skills/compactness in your project. Claude Code loads it when a task matches its description.

How do I install Compactness in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill compactness -a codex`. Or copy the skill folder (.claude/skills/math/topology/compactness in parcadei/Continuous-Claude-v3) into .agents/skills/compactness in your project. Codex loads it when a task matches its description.

Can I use Compactness 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 compactness -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/compactness, .gemini/skills/compactness, .github/skills/compactness and .opencode/skills/compactness in your project.

What does Compactness need to run?

Going by SKILL.md and its folder, Compactness needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Compactness 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 Compactness 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 Compactness use?

Compactness 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 Compactness use?

About 732 tokens (SKILL.md is roughly 2.9k 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 Compactness?

Skills that share tags, products or a category with Compactness: Sympy (zLanqing/codex-claude-academic-skills, 4.6k stars), Edu Analytic Geometry (wy51ai/edulab, 1.4k stars), Edu Solid Geometry (wy51ai/edulab, 1.4k stars) and Math Tools (ananddtyagi/cc-marketplace, 687 stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Compactness?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,940 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.