# On pseudocompact topological Brandt λ 0 -extensions of semitopological monoids

Topological Algebra and its Applications (2013)

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

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topOleg 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 -

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