list of common topologies

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 $\mathbb{Z},\mathbb{N},ℝ$)

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 can be found here (http://planetmath.org/FunctionSpaces).

1. Whitney topology (differential geometry)

2. Compact-open topology

Title	list of common topologies
Canonical name	ListOfCommonTopologies
Date of creation	2013-03-22 14:38:27
Last modified on	2013-03-22 14:38:27
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	5
Author	matte (1858)
Entry type	Topic
Classification	msc 54-00
Classification	msc 55-00
Classification	msc 22-00