Closed subsets of compact-like topological spaces

Bardyla, Serhii; Ravsky, Alex

doi:10.4995/agt.2020.12258

Cited by 6 publications

(4 citation statements)

References 25 publications

(26 reference statements)

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“…Stable and Γ-compact topological semigroups do not contain the bicyclic monoid [5,30,31]. The problem of embedding the bicyclic monoid into compact-like topological semigroups was studied in [6,7,11,29].…”

Section: ])mentioning

confidence: 99%

On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero

Гутік

Khylynskyi

2022

Topological Algebra and Its Applications

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Let 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofinite isometries of positive integers which contains Cscr;ℕ as a submonoid then every Hausdorff locally compact shift-continuous topology on S with adjoined zero is either compact or discrete. Also we show that the similar statement holds for a locally compact semitopological semigroup S with an adjoined compact ideal.

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Section: ])mentioning

confidence: 99%

On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero

Гутік

Khylynskyi

2022

Topological Algebra and Its Applications

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“…Stable and Γ-compact topological semigroups do not contain the bicyclic monoid [1,35,40]. The problem of embedding the bicyclic monoid into compact-like topological semigroups was studied in [4,5,8,25].…”

Section: Introductionmentioning

confidence: 99%

On a locally compact monoid of cofinite partial isometries of $\mathbb{N}$ with adjoined zero

Гутік¹,

Khylynskyi²

2021

Preprint

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Let C N be a monoid which is generated by the partial shift α : n → n+1 of the set of positive integers N and its inverse partial shift β : n+1 → n. In this paper we prove that if S is a submonoid of the monoid IN ∞ of all partial cofinite isometries of positive integers which contains C N as a submonoid then every Hausdorff locally compact shift-continuous topology on S with adjoined zero is either compact or discrete. Also we show that the similar statement holds for a locally compact semitopological semigroup S with an adjoined compact ideal.

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“…Stable and Γ-compact topological semigroups do not contain the bicyclic monoid [1,25,26]. The problem of embedding the bicyclic monoid into compact-like topological semigroups was studied in [3][4][5]17].…”

Section: Introductionmentioning

confidence: 99%

On the monoid of cofinite partial isometries of $\qq{N}^n$ with the usual metric

Гутік

Savchuk

2019

ПМГЦ

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In this paper we study the structure of the monoid IN n ∞ of cofinite partial isometries of the n-th power of the set of positive integers N with the usual metric for a positive integer n 2. We describe the elements of the monoid IN n ∞ as partial transformation of N n , the group of units and the subset of idempotents of the semigroup IN n ∞ , the natural partial order and Green's relations on IN n ∞ . In particular we show that the quotient semigroup IN n ∞ /C mg , where C mg is the minimum group congruence on IN n ∞ , is isomorphic to the symmetric group S n and D = J in IN n ∞ . Also, we prove that for any integer n 2 the semigroup IN n ∞ is isomorphic to the semidirect product S n ⋉ h (P ∞ (N n ), ∪) of the free semilattice with the unit (P ∞ (N n ), ∪) by the symmetric group S n .

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Closed subsets of compact-like topological spaces

Cited by 6 publications

References 25 publications

On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero

On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero

On a locally compact monoid of cofinite partial isometries of $\mathbb{N}$ with adjoined zero

On the monoid of cofinite partial isometries of $\qq{N}^n$ with the usual metric

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