A continuous group which has the topology of a T2-space
is a topological group. The simplest example is the group of real numbers under addition.

The homeomorphism group of any compact T2-space is a topological group when given the compact-open
topology. Also, any Lie group is a topological group.

## See also

Effective Action,

Free Action,

Group,

Group Orbit,

Group Representation,

Isotropy
Group,

Matrix Group,

Quotient
Space,

Transitive
*This entry contributed by Todd
Rowland*

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## Cite this as:

Rowland, Todd. "Topological Group." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/TopologicalGroup.html

## Subject classifications