Category:Definitions/Topological Groups
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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:
\((1)\) | $:$ | 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.
I
P
- Definitions/Profinite Groups (3 P)
Pages in category "Definitions/Topological Groups"
The following 18 pages are in this category, out of 18 total.