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.
 2.
 3.

4.
cocountable topology
New topologies from old ones
 1.
 2.
 3.
 4.

5.
inductive limit topology
Topologies on sets with more structure

1.
order topology (standard topologies on $\mathbb{Z},\mathbb{N},\mathbb{R}$)
 2.

3.
seminorm^{} topology (topological vector spaces^{})
 4.

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.
Title  list of common topologies 

Canonical name  ListOfCommonTopologies 
Date of creation  20130322 14:38:27 
Last modified on  20130322 14:38:27 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  5 
Author  matte (1858) 
Entry type  Topic 
Classification  msc 5400 
Classification  msc 5500 
Classification  msc 2200 