Examples/classes:
Types
Related concepts:
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 Seifert surface (named after Herbert Seifert) is an orientable surface whose boundary is a given knot or link. This concept may be extended to higher dimensions where a compact oriented -manifold forms the boundary of a higher-dimensional link, a disconnected union of copies of the -sphere as a submanifold of the -sphere.
Beware that there is also the un-related concept of:
See also:
Last revised on November 26, 2024 at 07:33:19. See the history of this page for a list of all contributions to it.