Results 51 to 60 of about 271 (88)
The regularity of quotient paratopological groups
Matematychni Studii, 2017 Let $H$ be a closed subgroup of a regular abelian paratopological group $G$. The group reflexion $G^\flat$ of $G$ is the group $G$ endowed with the strongest group topology, weaker that the original topology of $G$. We show that the quotient $G/H$ is Hausdorff (and regular) if $H$ is closed (and locally compact) in $G^\flat$.
Banakh, T., Ravsky, A.
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Cellularity in subgroups of paratopological groups
Topology and its Applications, 2015 A paratopological (semitopological) group is a group with a topology such that multiplication on the group is jointly (separately) continuous. In this paper, it is proved that every subgroup of a \(\sigma\)-compact \(T_1\) paratopological group has countable cellularity (but this conclusion fails for subgroups of \(\sigma\)-compact \(T_0 ...
Tkachenko, Mikhail G., Tomita, Artur H.
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Stationary Sets in Topological and Paratopological Groups
, 2012 We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This statement implies that if a monotonically normal space (in particular, any generalized ordered space) is a paratopological group then the space is ...
Buzyakova, Raushan Z., VURAL, ÇETİN
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A note on semitopological groups and paratopological groups
Topology and its Applications, 2015 \textit{M. Tkachenko} proved in [Topology Appl. 161, 364--376 (2014; Zbl 1287.54047)] that for every semitopological group \(G\) and every \(i\in\{0,1,2,3,3.5\}\), there exists a continuous homomorphism \(\varphi_{G,i}:G\to H\) onto a \(T_i\)- (resp., \(T_i\) \& \(T_1\)- for \(i\geq3\)) semitopological group \(H\) such that for every continuous mapping
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Cone topologies of paratopological groups
, 2014 This paper was updated and finally became a part of a larger paper arXiv 1003.5343 (v6), so please read and reference the last version of the latter paper instead of this (1406.2993)
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Pseudocompact paratopological groups that are topological
, 2014 This paper was updated and finally became a part of a larger paper arXiv 1003.5343 (v6), so please read and reference the last version of the latter paper instead of this (1406.2001)
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Neighborhood base at the identity of free paratopological groups
Topological Algebra and its Applications, 2013 Elfard Ali Sayed
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On free paratopological groups
Matematychni Studii, 2006 N. M. Pyrch, O. V. Ravsky
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Paratopological groups: Local versus global
Topology and its Applications, 2020An example is given in order to show that locally metrizable paratopological groups might be neither paracompact nor normal. This provides negative answers to questions previously posed in the field by \textit{A. Arhangel'skii} and \textit{M. Tkachenko} [Topological groups and related structures. Hackensack, NJ: World Scientific; Paris: Atlantis Press (
Li, Piyu, Mou, Lei, Xu, Yanqin
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