# Category:Topological Groups

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This category contains results about **Topological Groups**.

Definitions specific to this category can be found in **Definitions/Topological Groups**.

$\struct {G, \odot, \tau}$ is a **topological group** if and only if:

\((1)\) | $:$ | Continuous Group Product | $\odot: \struct {G, \tau} \times \struct {G, \tau} \to \struct {G, \tau}$ is a continuous mapping | ||||||

\((2)\) | $:$ | Continuous Inversion Mapping | $\iota: \struct {G, \tau} \to \struct {G, \tau}$ such that $\forall x \in G: \map \iota x = x^{-1}$ is also a continuous mapping |

where $\struct {G, \tau} \times \struct {G, \tau}$ is considered as $G \times G$ with the product topology.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Topological Groups"

The following 18 pages are in this category, out of 18 total.