Category:Topological Groups

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 3 subcategories, out of 3 total.

The following 17 pages are in this category, out of 17 total.

\((1)\)	$:$		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