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
algebraic topology – application of higher algebra and higher category theory to the study of (stable) homotopy theory
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
This page is about the article
Analysis Situs
Journal de l’École Polytechnique. (2). 1: 1–123
(1895)
original: gallica:12148/bpt6k4337198/f7
English translation by John Stillwell: pdf, pdf
which laid modern foundations of topology (such as introducing the notion and terminology of homeomorphisms) and introduced basic concepts of algebraic topology (such as singular homology) and of homotopy theory (such as the fundamental group).
See also:
Wikipedia, Analysis Situs_(paper)
Peter Hilton, Subjective History of Homology and Homotopy Theory, Mathematics Magazine 61 5 (1988) 282-291 $[$doi:10.2307/2689545$]$
Last revised on February 25, 2023 at 12:22:54. See the history of this page for a list of all contributions to it.