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Agent skill

Open Sets

by parcadei in parcadei/Continuous-Claude-v3

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

MITAuto-check: notes

Install Open Sets

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

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

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 open-sets --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/open-sets .claude/skills/open-sets && 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
open-sets
GitHub stars
3.9k
Used in
1 other repo
Token cost
~792 tokens
SKILL.md length
397 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

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

  • Works in 4 steps: Is f: X -> Y continuous? → Open Set Verification → Topological Properties → …
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Open Sets is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for open sets in topology

Its SKILL.md is about 790 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

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.

Example prompts

  • “/open-sets”

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 f: X -> Y continuous?
  2. Open Set Verification
  3. Topological Properties
  4. Continuity Tests

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

Open Sets loads about 792 tokens when it runs. Until then it costs about 16 tokens; SKILL.md has 397 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~16
When it runs · the whole SKILL.md, loaded when a task matches
~792

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). 397 words, ~792 tokens.

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

Open Sets

When to Use

Use this skill when working on open-sets problems in topology.

Decision Tree

  1. Is f: X -> Y continuous?

    • For metric spaces: x_n -> x implies f(x_n) -> f(x)?
    • For general spaces: f^(-1)(open) = open?
    • For products: Check each coordinate function
    • z3_solve.py prove "preimage_open"

  2. Open Set Verification

    • For metric spaces: for all x in U, exists epsilon > 0 with B(x,epsilon) subset U
    • z3_solve.py prove "ball_contained" with epsilon witnesses

  3. Topological Properties

    • Interior: int(A) = largest open subset of A
    • Closure: cl(A) = smallest closed superset of A
    • Boundary: bd(A) = cl(A) \ int(A)

  4. Continuity Tests

    • Epsilon-delta: for all epsilon > 0, exists delta > 0: d(x,a) < delta implies d(f(x),f(a)) < epsilon
    • z3_solve.py prove "epsilon_delta_bound"

Tool Commands

Z3_Preimage_Open
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "preimage_open"
Z3_Epsilon_Delta
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll(eps, Exists(delta, d(x,a) < delta implies d(f(x),f(a)) < eps))"
Z3_Ball_Contained
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "ball_contained"

Key Techniques

From indexed textbooks:

  • [Introduction to Topological Manifolds... (Z-Library)] Show that every local homeomorphism is an open map. Show that every homeomorphism is a local homeomorphism. Show that a bijective continuous open map is a homeomorphism.
  • [Introduction to Topological Manifolds... (Z-Library)] The key motivation behind the denition of this new kind of space is the open set criterion for continuity (Lemma A. Appendix), which shows that continuous functions between metric spaces can be detected knowing only the open sets. Motivated by this observation, we make the following denition.
  • [Introduction to Topological Manifolds... (Z-Library)] Suppose X is a set, and B is any collection of subsets of X whose union equals X. Let T be the collection of all unions of nite inter- sections of elements of B. Note that the empty set is the union of the empty collection of sets.
  • [Introduction to Topological Manifolds... (Z-Library)] The product topology is “associative” in the sense that the three prod- uct topologies X1 × X2 × X3, (X1 × X2) × X3, and X1 × (X2 × X3) on the set X1 × X2 × X3 are all equal. For any i and any points xj ∈ Xj, j = i, the map fi : Xi → X1 × · · × Xn given by fi(x) = (x1, . If for each i, Bi is a basis for the topology of Xi, then the set {B1 × · · · × Bn : Bi ∈ Bi} is a basis for the product topology on X1 × · · · × Xn.
  • [Introduction to Topological Manifolds... (Z-Library)] Here are some examples of closed subsets of familiar topological spaces. Any closed interval [a, b] ⊂ R is a closed set, as are the half-innite closed intervals [a, ∞) and (−∞, b]. Every subset of a discrete space is closed.
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/topology/open-sets 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.

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Manage Settingsasgeirtj/system_prompts_leaks69k—~3.1kAutomated safety check: PassCC0-1.0
Launch Strategyalirezarezvani/claude-skills28k—~1.4kAutomated safety check: PassMIT

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Questions about Open Sets

What does Open Sets do?

Problem-solving strategies for open sets in topology. An agent skill from parcadei/Continuous-Claude-v3. Open Sets is an agent skill from parcadei/Continuous-Claude-v3.

How do I install Open Sets in Claude Code?

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

How do I install Open Sets in Codex?

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

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

What does Open Sets need to run?

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

Does Open Sets 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 Open Sets 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 Open Sets use?

Open Sets 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 Open Sets use?

About 792 tokens (SKILL.md is roughly 3.2k 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 Open Sets?

Skills that share tags, products or a category with Open Sets: Good Strategy Bad Strategy (wondelai/skills, 2.4k stars), Product Strategy (phuryn/pm-skills, 27k stars), Vc Problem Solving (withkynam/vibecode-pro-max-kit, 1.1k stars) and Manage Settings (asgeirtj/system_prompts_leaks, 69k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Open Sets?

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.