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
symmetric monoidal (∞,1)-category of spectra
A topological algebra is equivalently
a topological ring which is also an associative algebra over some base topological ring;
an associative algebra internal to the category Top of topological spaces and continuous functions between them
an associative algebra structure on a topological space such that the algebra operations are continuous functions.
A Banach algebra is in particular a topological algebra.
Eduardo Dubuc, Horacio Porta, Convenient categories of topological algebras, Bull. Amer. Math. Soc., Volume 77, Number 6 (1971), 975-979 (Euclid:1183533170)
Last revised on July 22, 2018 at 20:08:52. See the history of this page for a list of all contributions to it.