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[parent] list of common topologies (Topic)

The aim of this entry is to give an overview of topologies commonly used in mathematics with links to the entries at Planetmath where these are discussed in greater detail.

Topologies on arbitrary sets

The below topologies show that any set can be endowed with a topology.
  1. discrete topology
  2. indiscrete topology
  3. cofinite topology
  4. cocountable topology

New topologies from old ones

  1. subspace topology
  2. quotient topology
  3. box topology
  4. product topology
  5. inductive limit topology

Topologies on sets with more structure

  1. order topology (standard topologies on $\sZ, \sN, \sR$ )
  2. metric topology
  3. seminorm topology (topological vector spaces)
  4. graph topology (graph theory)
  5. Zariski topology (algebraic geometry)

Topologies for functions spaces and mappings

An extensive list of function spaces can be found here.
  1. Whitney topology (differential geometry)
  2. Compact-open topology



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Cross-references: compact-open topology, differential geometry, Whitney topology, algebraic geometry, Zariski topology, graph theory, graph topology, topological vector spaces, seminorm, metric topology, standard topologies, order topology, inductive limit, product topology, box topology, quotient topology, subspace topology, cocountable topology, cofinite topology, indiscrete topology, discrete topology, PlanetMath, links, topologies
There is 1 reference to this entry.

This is version 2 of list of common topologies, born on 2004-09-24, modified 2004-09-25.
Object id is 6227, canonical name is ListCommonTopologies.
Accessed 2966 times total.

Classification:
AMS MSC: 54-00 (General topology :: General reference works )
 55-00 (Algebraic topology :: General reference works )
 22-00 (Topological groups, Lie groups :: General reference works )
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