# Category:Topological Groups

This category contains results about Topological Groups.
Definitions specific to this category can be found in Definitions/Topological Groups.

$\left({G, \odot, \tau}\right)$ is a topological group if and only if:

$(1): \quad \odot: \left({G, \tau}\right) \times \left({G, \tau}\right) \to \left({G, \tau}\right)$ is a continuous mapping
$(2): \quad \phi: \left({G, \tau}\right) \to \left({G, \tau}\right)$ such that $\forall x \in G: \phi \left({x}\right) = x^{-1}$ is also a continuous mapping

where $\left({G, \tau}\right) \times \left({G, \tau}\right)$ is considered as $G \times G$ with the product topology.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Topological Groups"

The following 16 pages are in this category, out of 16 total.