quantum algorithms:
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
Examples/classes:
Types
Related concepts:
In mathematics, the term quantum topology is used for the low-dimensional topology (such as knot theory) and related algebra (such as quantum groups) which is informed by Chern-Simons topological quantum field theory, and its various facets and generalizations.
David Yetter (ed.), Quantum Topology, World Scientific (1994) [doi:10.1142/2322]
Louis Kauffman, Quantum Topology and Quantum Computing, in: Samuel J. Lomonaco (ed.), Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, Proceedings of Symposia in Applied Mathematics 58, AMS (2002) [pdf, doi:10.1090/psapm/058]
(in relation to topological quantum computation)
See also:
Created on March 15, 2023 at 12:32:46. See the history of this page for a list of all contributions to it.