npx skills add parcadei/Continuous-Claude-v3 --skill compactness --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# 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)"
- When to Use
- Decision Tree
- Tool Commands
- Z3BoundedClosed
- SympyLimit
- SympyMaximum
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "bounded_and_closed" uv run python -m runtime.harness scripts/sympy_compute.py limit "a_n" --var n --at oo uv run python -m runtime.harness scripts/sympy_compute.py maximum "f(x)" --var x --domain "[a,b]"
What does the compactness skill do?
Problem-solving strategies for compactness in topology
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill compactness --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From parcadei/Continuous-Claude-v3, a repository with 3,879 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.