On pseudocompact topological Brandt λ⁰-extensions of semitopological monoids

• Autorzy: Oleg Gutik , Kateryna Pavlyk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Semitopological semigroup; Stone-Cˇ ech compactification; Bohr compactification; pseudocompact space; countably pracompact space; countably compact space; semigroup extension; category; full functor; representative functor

Kategorie tematyczne

• 22A15: Structure of topological semigroups
• 54H15: Transformation groups and semigroups

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2013
• Tom: 1
• Strony: 60-79

Daty

otrzymano

2012-11-26

zaakceptowano

2013-09-10

online

2013-12-31

Twórcy

autor

Oleg Gutik

• Department of Mechanics and Mathematics,
  National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine

autor

Kateryna Pavlyk

• Institute of Mathematics, University of Tartu,
  J. Liivi 2, 50409, Tartu, Estonia

Bibliografia

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Identyfikatory

DOI

10.2478/taa-2013-0007