# Topology

Anki flash cards structured around the notes

*General Topology*by Tom Leinster. They are published with the permission from Prof. Leinster.- Metric space
- Metric space. ε-balls
- Metric space. Open and closed sets
- Metric space. Unions and intersections of open sets
- Metric space. Sequence convergence
- Metric space. Function continuity
- Topology and topological space. Definition
- Finer and coarser topologies
- Neighbourhoods
- Closed subsets
- Hausdorff spaces
- Sequence convergence
- Continuous maps
- Homeomorphisms. Homeomorphic spaces.
- Basis
- Subbasis
- Compactness. Motivation
- Compactness
- Compactness. Examples
- Compactness. Subspaces
- Connectedness. Definition
- Connectedness Examples
- Connectedness. Equivalent formulations
- Connectedness. 4 lemmas
- Path connectedness. Definition
- Path-connectedness. 4 statements
- Connectedness, compactness and some fundamental theorems of calculus

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