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Topology
Topological Space
Subspace Topology
Manifold
Neighbourhood
Point-Set Topology/General Topology
Point-Free Topology
Topological Manifold
References
Every Metric Space Is Separable in Function Realizability. Andrej Bauer, Andrew Swan. 2019.
Synthetic Topology and Constructive Metric Spaces. Davorin Lesnik. 2010.
A Unified Theory of Function Spaces and Hyperspaces: Local Properties. S. Dolecki, F. Mynard. 2010.