Category:Definitions/Topological Groups

From ProofWiki
Jump to navigation Jump to search

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


$\left({G, \odot, \tau}\right)$ is a topological group if and only if:

$(1): \quad \odot: \left({G, \tau}\right) \times \left({G, \tau}\right) \to \left({G, \tau}\right)$ is a continuous mapping
$(2): \quad \phi: \left({G, \tau}\right) \to \left({G, \tau}\right)$ such that $\forall x \in G: \phi \left({x}\right) = x^{-1}$ is also a continuous mapping

where $\left({G, \tau}\right) \times \left({G, \tau}\right)$ is considered as $G \times G$ with the product topology.