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The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.
This is a list of useful examples in general topology, a field of mathematics. Alexandrov topology; ... This page was last edited on 5 April 2022, at 14:14 (UTC).
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. This is a list of topology topics. See also: Topology glossary; List of topologies; List of general topology topics; List of geometric topology topics
The trivial topology (or indiscrete topology) on a set X consists of precisely the empty set and the entire space X. Tychonoff A Tychonoff space (or completely regular Hausdorff space, completely T 3 space, T 3.5 space) is a completely regular T 0 space. (A completely regular space is Hausdorff if and only if it is T 0, so the terminology is ...
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms ...
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This category has the following 5 subcategories, out of 5 total. H. Homogeneous spaces (2 C, 18 P) M. ... List of topologies; Topologist's sine curve; Trivial topology;