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List of topologies

From Wikipedia, the free encyclopedia

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.

Widely known topologies

Counter-example topologies

The following topologies are a known source of counterexamples for point-set topology.

Hyperbolic geometry

Paradoxical spaces

Pathological embeddings of spaces


Topologies defined in terms of other topologies

Natural topologies

List of natural topologies.


Topologies of uniform convergence

This lists named topologies of uniform convergence.

Functional analysis

Operator topologies

Tensor products

Other induced topologies

  • Box topology
  • Duplication of a point: Let be a non-isolated point of let be arbitrary, and let Then is a topology on and x and d have the same neighborhood filters in In this way, x has been duplicated.[1]

Fractal spaces

Topologies related to other structures

Other topologies

See also


  1. ^ Wilansky 2008, p. 35.


This page was last edited on 3 August 2022, at 16:22
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