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On pseudocompact topological Brandt λ0-extensions of semitopological monoids

100%

Gutik O., Pavlyk K.

Topological Algebra and its Applications

2013

tom 1

60-79

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.

Isometry groups of non standard metric products

64%

Oliynyk B.

Open Mathematics

2013

tom 11

nr 2

264-273

We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.

Ograniczanie wyników

1 Open Mathematics

1 Topological Algebra and its Applications

1 Gutik O.

1 Oliynyk B.

1 Pavlyk K.

2 2013

Wyniki wyszukiwania

On pseudocompact topological Brandt λ0-extensions of semitopological monoids

Isometry groups of non standard metric products