On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids

Oleg Gutik; Kateryna Pavlyk

Topological Algebra and its Applications (2013)

  • Volume: 1, page 60-79
  • ISSN: 2299-3231

Abstract

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In the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.

How to cite

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Oleg Gutik, and Kateryna Pavlyk. " On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids ." Topological Algebra and its Applications 1 (2013): 60-79. <http://eudml.org/doc/267070>.

@article{OlegGutik2013,
abstract = {In the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.},
author = {Oleg Gutik, Kateryna Pavlyk},
journal = {Topological Algebra and its Applications},
keywords = {Semitopological semigroup; Stone-Cˇ ech compactification; Bohr compactification; pseudocompact space; countably pracompact space; countably compact space; semigroup extension; category; full functor; representative functor; semitopological semigroup; Stone-Čech compactification},
language = {eng},
pages = {60-79},
title = { On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids },
url = {http://eudml.org/doc/267070},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Oleg Gutik
AU - Kateryna Pavlyk
TI - On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids
JO - Topological Algebra and its Applications
PY - 2013
VL - 1
SP - 60
EP - 79
AB - In the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.
LA - eng
KW - Semitopological semigroup; Stone-Cˇ ech compactification; Bohr compactification; pseudocompact space; countably pracompact space; countably compact space; semigroup extension; category; full functor; representative functor; semitopological semigroup; Stone-Čech compactification
UR - http://eudml.org/doc/267070
ER -

References

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