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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).
11
votes
0
answers
268
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A ZFC-example of a countably compact paratopological group which is not a topological group
Problem. Does there exist a ZFC-example of a countably compact Hausdorff paratopological group which is not a topological group?
(The problem posed 27 May 2015 by Alexander Ravsky on page 9 of Vo …
6
votes
1
answer
376
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Pontriagin reflexivity of the character group
For an Abelian topological group $G$ by $G^{\wedge}$ we denote the Pontryagin dual of $G$, i.e. the group of continuous homomorphisms $G\to\mathbb T:=\{z\in\mathbb C:|z|=1\}$. The group $G^{\wedge}$ i …
8
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0
answers
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A basis of the Banach space $L^p(\mathbb T^\omega)$ consisting of characters
Problem: For $1<p<\infty$, $p\ne 2$, has the complex Banach space $L^p(\mathbb T^\omega)$ got a Schauder basis consisting of characters of the compact topological group $\mathbb T^\omega$?
(This …