npx skills add parcadei/Continuous-Claude-v3 --skill open-sets --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.
# 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 pro
- When to Use
- Decision Tree
- Tool Commands
- Z3PreimageOpen
- Z3EpsilonDelta
- Z3BallContained
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "preimage_open" 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))" uv run python -m runtime.harness scripts/z3_solve.py prove "ball_contained"
What does the open-sets skill do?
Problem-solving strategies for open sets in topology
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill open-sets --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 3,885 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.