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.