On pseudocompact topological Brandt λ0-extensions of semitopological monoids

Oleg Gutik 1  and Kateryna Pavlyk 2
  • 1 Department of Mechanics and Mathematics, National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine
  • 2 Institute of Mathematics, University of Tartu, J. Liivi 2, 50409, Tartu, Estonia


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.

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