Pseudocompact Primitive Topological Inverse Semigroups

Гутік, Олег; Pavlyk, Kateryna

doi:10.1007/s10958-014-2087-5

Cited by 5 publications

(10 citation statements)

References 18 publications

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“…Example 1 of [6] shows that inversion on a quasi-regular inverse countably compact topological semigroup in which maximal subgroups are topological groups is not continuous. Also Corollary 3.23 and Proposition 2.8 from [17] imply that a quasi-regular primitive inverse feebly compact topological semigroup is Tychonoff. Also, Corollary 3.23 implies…”

Section: Proof Suppose For a Contradiction That There Exists An Openmentioning

confidence: 89%

“…In the paper [17] the structure of feebly compact primitive topological inverse semigroups is described and it is shown that the Tychonoff product of an arbitrary non-empty family of feebly compact primitive topological inverse semigroups is feebly compact. Also, it is proved that the Stone-Čech compactification of a feebly compact primitive topological inverse semigroup has a natural structure of a compact primitive topological inverse semigroup.…”

Section: Introductionmentioning

confidence: 99%

“…The structure of primitive Hausdorff feebly compact topological inverse semigroup is described in [17]. It is proved that every primitive Hausdorff feebly compact topological inverse semigroup S is topologically isomorphic to the orthogonal sum i∈I B λ i (G i ) of topological Brandt λ i -extensions B λ i (G i ) of pseudocompact topological groups G i in the class of topological inverse semigroups for some finite cardinals λ i 1.…”

Section: Introductionmentioning

confidence: 99%

“…It is proved that every primitive Hausdorff feebly compact topological inverse semigroup S is topologically isomorphic to the orthogonal sum i∈I B λ i (G i ) of topological Brandt λ i -extensions B λ i (G i ) of pseudocompact topological groups G i in the class of topological inverse semigroups for some finite cardinals λ i 1. Also, [17] contains a description of a base of the topology of a primitive Hausdorff feebly compact topological inverse semigroup. Similar results for primitive Hausdorff countably compact topological inverse semigroups and Hausdorff compact topological inverse semigroups were obtained in [7].…”

Section: Introductionmentioning

confidence: 99%

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On feebly compact inverse primitive (semi)topological semigroups

Гутік

Ravsky

2013

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We study the structure of inverse primitive feebly compact semitopological and topological semigroups. We find conditions when the maximal subgroup of an inverse primitive feebly compact semitopological semigroup S is a closed subset of S and describe the topological structure of such semiregular semitopological semigroups. Later we describe the structure of feebly compact topological Brandt λ 0 -extensions of topological semigroups and semiregular (quasi-regular) primitive inverse topological semigroups. In particular we show that inversion in a quasi-regular primitive inverse feebly compact topological semigroup is continuous. Also an analogue of Comfort-Ross Theorem is proved for such semigroups: a Tychonoff product of an arbitrary family of primitive inverse semiregular feebly compact semitopological semigroups with closed maximal subgroups is feebly compact. We describe the structure of the Stone-Čech compactification of a Hausdorff primitive inverse countably compact semitopological semigroup S such that every maximal subgroup of S is a topological group.

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Section: Proof Suppose For a Contradiction That There Exists An Openmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On feebly compact inverse primitive (semi)topological semigroups

Гутік

Ravsky

2013

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“…In the paper [16] it is described the structure of pseudocompact primitive topological inverse semigroups and it is shown that the Tychonoff product of an arbitrary non-empty family of pseudocompact primitive topological inverse semigroups is pseudocompact. Also, there is proved that the Stone-Čech compactification of a pseudocompact primitive topological inverse semigroup has a natural structure of a compact primitive topological inverse semigroup.…”

Section: Introductionmentioning

confidence: 99%

Pseudocompactness, Products, and Topological Brandt λ0 -Extensions of Semitopological Monoids

Гутік

Ravsky²

2017

J Math Sci

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In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, ω-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff products of pseudocompact (and countably compact) topological Brandt λ 0 i -extensions of semitopological monoids with zero. In particular we show that ifa family of Hausdorff pseudocompact topological Brandt λ 0 i -extensions of pseudocompact semitopological monoids with zero such that the Tychonoff product {S i : i ∈ I } is a pseudocompact space then the direct product B 0 λi (S i ), τ 0 B(Si) : i ∈ I endowed with the Tychonoff topology is a Hausdorff pseudocompact semitopological semigroup. Date: September 24, 2018. 2010 Mathematics Subject Classification. Primary 22A15, 54H10. Key words and phrases. Semigroup, Brandt λ 0 -extension, semitopological semigroup, topological Brandt λ 0 -extension, pseudocompact space, countably compact space, countably pracompact space, sequentially compact space, ω-bounded space, totally countably compact space, countable pracompact space, sequential pseudocompact space.

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Quasi-multipliers on topological semigroups and their Stone–Čech compactification

2021

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In this paper, we introduce and study the notion of quasi-multipliers on a semi-topological semigroup [Formula: see text]. The set of all quasi-multipliers on [Formula: see text] is denoted by [Formula: see text]. First, we study the problem of extension of quasi-multipliers on topological semigroups to its Stone–Čech compactification. Indeed, we prove if [Formula: see text] is a topological semigroup such that [Formula: see text] is pseudocompact, then [Formula: see text] can be regarded as a subset of [Formula: see text] Moreover, with an extra condition we describe [Formula: see text] as a quotient subsemigroup of [Formula: see text] Finally, we investigate quasi-multipliers on topological semigroups, its relationship with multipliers and give some concrete examples.

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Pseudocompact Primitive Topological Inverse Semigroups

Cited by 5 publications

References 18 publications

On feebly compact inverse primitive (semi)topological semigroups

On feebly compact inverse primitive (semi)topological semigroups

Pseudocompactness, Products, and Topological Brandt λ0 -Extensions of Semitopological Monoids

Quasi-multipliers on topological semigroups and their Stone–Čech compactification

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