banach-spaces
Problem-solving strategies for banach spaces in functional analysis
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces --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.
# Banach Spaces ## When to Use Use this skill when working on banach-spaces problems in functional analysis. ## Decision Tree 1. **Verify Banach space** - Complete normed vector space - Check: every Cauchy sequence converges - `z3_solve.py prove "completeness"` 2. **Hahn-Banach Theorem** - Extend bounded linear functionals - Separate convex sets - `z3_solve.py prove "extension_exists"` 3. **Open Mapping Theorem** - Surjective bounded operator between Banach spaces is open - Consequence: bounded inverse exists - `z3_solve.py prove "open_mapping"` 4. **Closed Graph Theorem** - T: X -> Y has closed graph implies T bounded - Strategy: verify graph closure, conclude boundedness - `z3_solve.py prove "closed_graph_implies_bounded"` 5. **Uniform Boundedness Principle** - Pointwise bounded family of operators is uniformly bounded - Application: prove operator families are bounded ## Tool Commands ### Z3_Completeness ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "cauchy_sequence implies convergent" ``` ### Z3_Open_Mapping ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "T_surjective_bounded implies T_open" ``` ### Z3_Closed_Graph ```bash uv run python
- When to Use
- Decision Tree
- Tool Commands
- Z3Completeness
- Z3OpenMapping
- Z3ClosedGraph
- SympyNorm
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "cauchy_sequence implies convergent" uv run python -m runtime.harness scripts/z3_solve.py prove "T_surjective_bounded implies T_open" uv run python -m runtime.harness scripts/z3_solve.py prove "graph_closed implies T_bounded" uv run python -m runtime.harness scripts/sympy_compute.py simplify "norm(alpha*x + beta*y)"
What does the banach-spaces skill do?
Problem-solving strategies for banach spaces in functional analysis
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill banach-spaces --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.