Category:Definitions/Topological Groups

This category contains definitions related to Topological Groups.
Related results can be found in Category:Topological Groups.

$\struct {G, \odot, \tau}$ is a topological group if and only if the following conditions are fulfilled:

$(1)$	$:$		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.

The following 19 pages are in this category, out of 19 total.