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Results tagged with topological-groups
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user 2508
A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).
18
votes
Does homeomorphic and isomorphic always imply homeomorphically isomorphic?
The Banach spaces $c_{0}$ and $\ell_{2}$ may be viewed as isomorphic
Abelian groups, that are also homeomorphic (due to Kadec). Still,
they are clearly not isomorphic as topological groups.
- 4,060
12
votes
Accepted
Sequential topological vector spaces
The space of tempered distributions is sequential (for its usual strong topology). See, e.g., Dudley, and the references therein.
- 4,060