Cardinal invariants of paratopological groups

Iván Sánchez

Topological Algebra and its Applications (2013)

  • Volume: 1, page 37-45
  • ISSN: 2299-3231

Abstract

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We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.

How to cite

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Iván Sánchez. "Cardinal invariants of paratopological groups." Topological Algebra and its Applications 1 (2013): 37-45. <http://eudml.org/doc/267157>.

@article{IvánSánchez2013,
abstract = {We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.},
author = {Iván Sánchez},
journal = {Topological Algebra and its Applications},
keywords = {Paratopological group; Totally ω-narrow; Index of regularity; Weak Lindelöf number; Hausdorff number; Symmetry number; Regular Gσ-diagonal; paratopological group; semitopological group; cardinal invariant; totally narrow; index of regularity; weak Lindelöf number; symmetry number; regular -diagonal},
language = {eng},
pages = {37-45},
title = {Cardinal invariants of paratopological groups},
url = {http://eudml.org/doc/267157},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Iván Sánchez
TI - Cardinal invariants of paratopological groups
JO - Topological Algebra and its Applications
PY - 2013
VL - 1
SP - 37
EP - 45
AB - We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.
LA - eng
KW - Paratopological group; Totally ω-narrow; Index of regularity; Weak Lindelöf number; Hausdorff number; Symmetry number; Regular Gσ-diagonal; paratopological group; semitopological group; cardinal invariant; totally narrow; index of regularity; weak Lindelöf number; symmetry number; regular -diagonal
UR - http://eudml.org/doc/267157
ER -

References

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