Link Invariants
Examples
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
The Vassiliev skein relation is a way to extend knot invariants to singular knots (at least, to singular knots where the only singularities are double points). If $v$ is a knot invariant that takes values in an abelian group, then it is extended to singular knots using the relation
where $L_d$ is a singular knot with a double point and $L_+$, respectively $L_-$, are formed from $L_d$ by replacing the double point by a positively oriented, respectively negatively oriented, crossing.
General discussion includes
Discussion in the context of quantization of 3d Chern-Simons theory includes
Razvan Gelca, Alejandro Uribe, From classical theta functions to topological quantum field theory (arXiv:1006.3252, slides pdf)
Razvan Gelca, Alejandro Uribe, Quantum mechanics and non-abelian theta functions for the gauge group $SU(2)$ (arXiv:1007.2010)
Last revised on July 18, 2015 at 10:33:30. See the history of this page for a list of all contributions to it.