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
A light profinite set is a countable limit of finite sets.
Light profinite sets are used to construct light condensed sets in condensed mathematics
The category of light profinite sets is equivalent to the opposite of the category of countably presented Boolean algebras.
Dustin Clausen, Peter Scholze, Analytic Stacks, YouTube playlist, website
David Wärn, On internally projective sheaves of groups (arXiv:2409.12835)
What does the topos of (light) condensed sets classify? (MathOverflow)
Last revised on December 6, 2024 at 16:53:53. See the history of this page for a list of all contributions to it.