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Prove compactness in topology v1.0.0

Use this resource to prove that a set is compact in topology

New

  • 397 downloads
  • 138 likes
  • 211 saves

Free

Install with the CLI

In a terminal, from the folder you want:

npx --yes palatekit@latest install topology-compactness-proofs

With no option, the skill goes to ~/.agents/skills/; add --agent claude-code (or codex, cursor…) to target an agent.

First time: connect the CLI with

npx --yes palatekit@latest login

The agent steers the compactness proof toward Heine-Borel, the sequential criterion or Tychonoff's theorem for products, then checks bounds and limits with SymPy and Z3. You get a structured proof.

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Updated November 2, 2026

Card for the “Prove compactness in topology” skill

Details

Works in
Install guides
Generates with
Your agent's model
Licence
MIT

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What you get

  • SKILL.md: decision tree (Heine-Borel, sequential, products)
  • SKILL.md: Z3 commands (closed and bounded) and SymPy (limit, maximum)

Good fit for

  • You need to show that a set is compact
  • You are reviewing the Heine-Borel theorem

Not for

    Tags

    • compactness
    • topology
    • heine-borel
    • proof

    About

    You say

    “Prove that the interval [0,1] is compact.”

    Card for the “Prove compactness in topology” skill

    Skill published by parcadei under the MIT license, delivered in its original version.

    Show more

    How to use it

    1. Install the skill in your agent's skills folder
    2. Ask your agent to prove that a set is compact in topology
    3. Review and adjust the result

    Content preview

    Files

    • LICENSE1.1 KB
    • NOTICE-PALATEKIT.md0.5 KB
    • SKILL.md2.9 KB

    Origin and licence

    Listed unmodified

    Author
    parcadei
    Source
    github.com/parcadei/continuous-claude-v3/tree/d07ff4b06b62f43771bc0c927d0211b734d6149e/.claude/skills/math/topology/compactness
    Licence
    MIT

    Notice

    « compactness » (parcadei, MIT) livré dans sa version d'origine : fiche en français et en anglais par PalateKit.

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