topology
Properties of spaces and continuity
Datos de origen
- Repositorio
- ffsshhttiikk/opencode-agents-skills
- Última actividad en el origen
- 28 de febrero de 2026 a las 22:55
- Idioma detectado de SKILL.md
- inglés
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- 3
- Forks
- 2
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SKILL.md
Instrucciones de origen · Vista previa de solo lectura- name
- topology
- description
- Properties of spaces and continuity
- license
- MIT
- compatibility
- opencode
- metadata
- {"audience":"mathematicians","category":"mathematics"}
## What I do
- Analyze topological spaces and continuity
- Work with open and closed sets
- Study compactness and connectedness
- Apply homotopy and homology groups
- Analyze metric spaces
- Study fixed point theorems
## When to use me
When analyzing spatial properties that are preserved under continuous deformations.
## Key Concepts
- **Topological Space**: Set with collection of open sets satisfying union/finite intersection closure
- **Continuous Function**: f^{-1}(open) is open; preserves topological properties
- **Homeomorphism**: Bijective continuous map with continuous inverse
- **Compactness**: Every open cover has finite subcover; Heine-Borel in ℝⁿ
- **Connectedness**: Cannot be partitioned into two nonempty open sets
- **Homotopy**: Continuous deformation between maps; homotopy equivalence
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