# Cardinal invariants of paratopological groups

Topological Algebra and its Applications (2013)

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

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topIván 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 -

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