npx skills add parcadei/Continuous-Claude-v3 --skill connectedness --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.
# Connectedness ## When to Use Use this skill when working on connectedness problems in topology. ## Decision Tree 1. **Is X connected?** - Strategy 1 - Contradiction: * Assume X = U union V where U, V are disjoint, non-empty, and open * Derive a contradiction - Strategy 2 - Path connectedness: * Show for all x,y in X, exists continuous path f: [0,1] -> X with f(0)=x, f(1)=y - Strategy 3 - Fan lemma: * If {A_i} are connected sharing a common point, then union A_i is connected 2. **Connectedness Proofs** - Show no separation exists - `z3_solve.py prove "no_separation"` - Use intermediate value theorem for R subsets 3. **Path Connectedness** - Construct explicit path: f(t) = (1-t)x + ty for convex sets - `sympy_compute.py simplify "(1-t)*x + t*y"` to verify path 4. **Components** - Connected component: maximal connected subset containing x - Path component: maximal path-connected subset containing x ## Tool Commands ### Z3_No_Separation ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "no_separation" ``` ### Sympy_Path ```bash uv run python -m runtime.harness scripts/sympy_compute.py simplify "(1-t)*x + t*y" ``` ### Z3_Ivt ```bash uv run python -m runtime.harness sc
- When to Use
- Decision Tree
- Tool Commands
- Z3NoSeparation
- SympyPath
- Z3Ivt
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "no_separation" uv run python -m runtime.harness scripts/sympy_compute.py simplify "(1-t)*x + t*y" uv run python -m runtime.harness scripts/z3_solve.py prove "intermediate_value"
What does the connectedness skill do?
Problem-solving strategies for connectedness in topology
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill connectedness --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.