# Topology

> Properties of spaces and continuity

- Skill: `ffsshhttiikk/topology` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ffsshhttiikk/topology`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ffsshhttiikk/topology/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: ffsshhttiikk (https://skillmd.com/u/ffsshhttiikk)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ffsshhttiikk/topology

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## 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