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Prove connectedness in topology v1.0.0

Use this resource to prove that a space is connected in topology

New

  • 374 downloads
  • 138 likes
  • 186 saves

Free

Install with the CLI

In a terminal, from the folder you want:

npx --yes palatekit@latest install topology-connectedness-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 a connectedness proof: contradiction with a separation, continuous paths or the fan lemma. It checks the steps with Z3 and SymPy and invokes the intermediate value theorem where it applies. You get a structured proof.

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Updated November 2, 2026

Card for the “Prove connectedness 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 (contradiction, paths, fan lemma)
  • SKILL.md: Z3 commands (no separation, IVT) and SymPy (path)

Good fit for

  • You need to show that a space is connected
  • You are reviewing connected components

Not for

    Tags

    • connectedness
    • topology
    • paths
    • proof

    About

    You say

    “Show that the interval [0,1] is connected.”

    Card for the “Prove connectedness 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 space is connected in topology
    3. Review and adjust the result

    Content preview

    Files

    • LICENSE1.1 KB
    • NOTICE-PALATEKIT.md0.5 KB
    • SKILL.md3.6 KB

    Origin and licence

    Listed unmodified

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

    Notice

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

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