topology (point-set topology, point-free topology)
see also differential topology, algebraic topology, functional analysis and topological homotopy theory
Basic concepts
fiber space, space attachment
Extra stuff, structure, properties
Kolmogorov space, Hausdorff space, regular space, normal space
sequentially compact, countably compact, locally compact, sigma-compact, paracompact, countably paracompact, strongly compact
Examples
Basic statements
closed subspaces of compact Hausdorff spaces are equivalently compact subspaces
open subspaces of compact Hausdorff spaces are locally compact
compact spaces equivalently have converging subnet of every net
continuous metric space valued function on compact metric space is uniformly continuous
paracompact Hausdorff spaces equivalently admit subordinate partitions of unity
injective proper maps to locally compact spaces are equivalently the closed embeddings
locally compact and second-countable spaces are sigma-compact
Theorems
Analysis Theorems
constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
Topological signal processing is the development and application of algebraic topology to the field of signal processing.
Michael Robinson. Topological Signal Processing, 2014 (doi:10.1007/978-3-642-36104-3)
Sergio Barbarossa, Stefania Sardellitti. Topological Signal Processing over Simplicial Complexes, 2020 (arXiv:1907.11577)
Elvin Isufi, Geert Leus, Baltasar Beferull-Lozano, Sergio Barbarossa, Paolo Di Lorenzo. Topological Signal Processing and Learning: Recent Advances and Future Challenges, 2024 (arXiv:2412.01576)
Created on October 18, 2025 at 03:04:51. See the history of this page for a list of all contributions to it.