# 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. 1.
2. 2.
3. 3.
4. 4.

cocountable topology

## New topologies from old ones

1. 1.
2. 2.
3. 3.
4. 4.
5. 5.

inductive limit topology

## Topologies on sets with more structure

1. 1.

order topology (standard topologies on $\mathbb{Z},\mathbb{N},\mathbb{R}$)

2. 2.
3. 3.
4. 4.
5. 5.

## Topologies for functions spaces and mappings

An extensive list of can be found here (http://planetmath.org/FunctionSpaces).

1. 1.

Whitney topology (differential geometry)

2. 2.
Title list of common topologies ListOfCommonTopologies 2013-03-22 14:38:27 2013-03-22 14:38:27 matte (1858) matte (1858) 5 matte (1858) Topic msc 54-00 msc 55-00 msc 22-00