On feebly compact paratopological groups

Банах, Тарас; Ravsky, Alex

doi:10.1016/j.topol.2020.107363

Cited by 15 publications

(11 citation statements)

References 48 publications

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“…This research explained the definition of fg-disconnected space and compactly fg-closed set. Also, we proved the obtained results based on the experimental methodology (Banakh & Ravsky, 2020). However, the proposed method is described in section 3; we debate and appraise the experiment results in section 4 and the conclusion in Section 5.…”

Section: Introductionmentioning

confidence: 61%

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The effect of some of spaces and sets of topology on the types of digital images

Shaaban

Khudayir²

2021

ACJ

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There is a growing interest in studying and improving the characteristics of images and objects in the e-commerce environment. Digital topology is concerned with dealing with the properties and features of two-dimensional (2D) or three-dimensional (3D) digital images such as borders, shapes, the intensity of illumination, and other characteristics. This paper aims to introduce and study new classes of fg-disconnected space and compactly fg-closed set, which could impact the brightness and brightness of the internal components of the types of color images, gray and binary. The paper also aims to find the effect of implementing fg-disconnected space and compactly fg-closed set to determine the brightness and brightness of the internal components of the types of color images, gray and binary. Each research plate contains 30 images of each type of image. Ten different images were chosen at the same time to be analyzed and executed using the proposed system based on MATLAB software. The study proved that higher brightness and light will disappear and delete the components of the image of any kind. This aimed to make the image white and opposite color, the greater darkness, and luminescence will make the picture color mysterious and turn to black.

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Section: Introductionmentioning

confidence: 61%

“…This section introduces the concepts fg-disconnected space as well as compactly-fg-closed set and their properties (Banakh & Ravsky, 2020).…”

Section: Theorems and Definitionsmentioning

confidence: 99%

The effect of some of spaces and sets of topology on the types of digital images

Shaaban

Khudayir²

2021

ACJ

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“…nonempty open subsets of G. By [14, Proposition 2.9], each ω-pseudobounded 2-pseudocompact paratopological group is pseudobounded. Since each 2-pseudocompact left topological group is feebly compact and Baire (by Proposition 3.13 and Lemma 3.7 from [4]), the following proposition generalizes this result.…”

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confidence: 60%

“…We claim that S = G. Indeed, following [4, Section 5.1], consider a (not necessarily Hausdorff) paratopological group G S whose topology consists of the sets A + S where A ⊆ G is any subset. Since the topology of the group G S is weaker than the topology of G and G is precompact, the group G S is precompact too, and so by Proposition 5.8 from [4], S is a subgroup of G. Since G is nondiscrete, U contains cosets a + Z for arbitrarily small positive numbers a, so S is dense in…”

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confidence: 99%

On pseudobounded and premeage paratopological groups

Ravsky

Банах

2021

Mat. Stud.

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Let $G$ be a paratopological group.Following F.~Lin and S.~Lin, we say that the group $G$ is pseudobounded,if for any neighborhood $U$ of the identity of $G$,there exists a natural number $n$ such that $U^n=G$.The group $G$ is $\omega$-pseudobounded,if for any neighborhood $U$ of the identity of $G$, the group $G$ is aunion of sets $U^n$, where $n$ is a natural number.The group $G$ is premeager, if $G\ne N^n$ for any nowhere dense subset $N$ of$G$ and any positive integer $n$.In this paper we investigate relations between the above classes of groups andanswer some questions posed by F. Lin, S. Lin, and S\'anchez.

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“…Example 4.9. In [BR2,Ex. 3] it is constructed a monothetic second countable paratopological group G such that each power of G is countably pracompact but G is not a topological group.…”

Section: Embedded Variationsmentioning

confidence: 99%

Positive answers to Koch’s problem in special cases

Банах

Bardyla

Guran

et al. 2020

Topological Algebra and Its Applications

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A topological semigroup is monothetic provided it contains a dense cyclic subsemigroup. The Koch problem asks whether every locally compact monothetic monoid is compact. This problem was opened for more than sixty years, till in 2018 Zelenyuk obtained a negative answer. In this paper we obtain a positive answer for Koch's problem for some special classes of topological monoids. Namely, we show that a locally compact monothetic topological monoid is a compact topological group if and only if S is a submonoid of a quasitopological group if and only if S has open shifts if and only if S is non-viscous in the sense of Averbukh. The last condition means that any neighborhood U of the identity 1 of S and for any element a ∈ S there exists a neighborhood V of a such that any element x ∈ S with (xV ∪ V x) ∩ V = ∅ belongs to the neighborhood U of 1.

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On feebly compact paratopological groups

Cited by 15 publications

References 48 publications

The effect of some of spaces and sets of topology on the types of digital images

The effect of some of spaces and sets of topology on the types of digital images

On pseudobounded and premeage paratopological groups

Positive answers to Koch’s problem in special cases

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