List of topologies

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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.

Contents

Discrete and indiscrete

Cardinality and ordinals

Finite spaces

Integers

Fractals and Cantor set

Orders

Manifolds and complexes

Hyperbolic geometry

Paradoxical spaces

Unique

Embeddings and maps between spaces

Counter-examples (general topology)

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

Topologies defined in terms of other topologies

Natural topologies

List of natural topologies.

Compactifications

Compactifications include:

Topologies of uniform convergence

This lists named topologies of uniform convergence.

Other induced topologies

Functional analysis

Operator topologies

Tensor products

Probability

Other topologies

See also

Citations

    References