Weak continuity properties of topologized groups

J. Cao; R. Drozdowski; Zbigniew Piotrowski

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 1, page 133-148
  • ISSN: 0011-4642

Abstract

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We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if ( G , · , τ ) is a regular right (left) semitopological group with dev ( G ) < Nov ( G ) such that all left (right) translations are feebly continuous, then ( G , · , τ ) is a topological group. This extends several results in literature.

How to cite

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Cao, J., Drozdowski, R., and Piotrowski, Zbigniew. "Weak continuity properties of topologized groups." Czechoslovak Mathematical Journal 60.1 (2010): 133-148. <http://eudml.org/doc/37996>.

@article{Cao2010,
abstract = {We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if $(G, \cdot ,\tau )$ is a regular right (left) semitopological group with $\mathop \{\{\rm dev\}\}(G)<\mathop \{\{\rm Nov\}\}(G)$ such that all left (right) translations are feebly continuous, then $(G,\cdot ,\tau )$ is a topological group. This extends several results in literature.},
author = {Cao, J., Drozdowski, R., Piotrowski, Zbigniew},
journal = {Czechoslovak Mathematical Journal},
keywords = {developability number; feebly continuous; nearly continuous; Novak number; paratopological group; semitopological group; topological group; developability number; feebly continuous; nearly continuous; Novak number; paratopological group; semitopological group; topological group},
language = {eng},
number = {1},
pages = {133-148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak continuity properties of topologized groups},
url = {http://eudml.org/doc/37996},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Cao, J.
AU - Drozdowski, R.
AU - Piotrowski, Zbigniew
TI - Weak continuity properties of topologized groups
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 133
EP - 148
AB - We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if $(G, \cdot ,\tau )$ is a regular right (left) semitopological group with $\mathop {{\rm dev}}(G)<\mathop {{\rm Nov}}(G)$ such that all left (right) translations are feebly continuous, then $(G,\cdot ,\tau )$ is a topological group. This extends several results in literature.
LA - eng
KW - developability number; feebly continuous; nearly continuous; Novak number; paratopological group; semitopological group; topological group; developability number; feebly continuous; nearly continuous; Novak number; paratopological group; semitopological group; topological group
UR - http://eudml.org/doc/37996
ER -

References

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