Compactness and completeness in partial metric spaces

Mykhaylyuk, Volodymyr; Myronyk, Vadym

doi:10.1016/j.topol.2019.106925

Cited by 11 publications

(5 citation statements)

References 16 publications

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“…Since the time of Matthews' work [16] publication, there have emerged many works investigating purely mathematical side of partial metric spaces. For example, there have appeared variants of BCP for partial metric spaces [1,4,10,20], results concerning the issue of completeness of a partial metric space [7,8,18], or, only recently, theorems relating sequential compactness and compactness of a partial metric space [3,18].…”

Section: P Maćkowiak Results Mathmentioning

confidence: 99%

A Converse of the Banach Contraction Principle for Partial Metric Spaces and the Continuum Hypothesis

Maćkowiak

2023

Results Math

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Section: P Maćkowiak Results Mathmentioning

confidence: 99%

A Converse of the Banach Contraction Principle for Partial Metric Spaces and the Continuum Hypothesis

Maćkowiak

2023

Results Math

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“…Compactness is a property in metric spaces. A metric space (X, ρ) is said to be totally bounded (or precompact) if, for every ϵ > 0, the space X can be covered by a finite family of open balls of radius ϵ [5]. A metric space X is said to be sequentially compact if every sequence (x n ) ∞ n=1 of points in X has a convergent subsequence [6].…”

Section: Introductionmentioning

confidence: 99%

On Some Aspects of Compactness in Metric Spaces

Isabu,

Ojiema

2024

ASAREV

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In this paper, we investigate the generalizations of the concepts from Heine-Borel Theorem and the Bolzano-Weierstrass Theorem to metric spaces. We show that the metric space X is compact if every open covering has a finite subcovering. This abstracts the Heine-Borel property. Indeed, the Heine-Borel Theorem states that closed bounded subsets of the real line R are compact. In this study, we rephrase compactness in terms of closed bounded subsets of the real line R, that is, the Bolzano-Weierstrass theorem. Let X be any closed bounded subset of the real line. Then any sequence (xn) of the points of X has a subsequence converging to a point of X. We have used these interesting theorems to characterize compactness in metric spaces.

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“…The developed concept of the fixed-point theorem in metric partial space has been widely studied by researchers (see (Kir Mehmet, 2016)- (Bugajewski & Wang, 2020)). Study about compactness and completeness in metric partial space to research about orthogonality in metric space has also been investigated (see (Mykhaylyuk & Myronyk, 2019), (Senapati, 2018)).…”

Section: Introductionmentioning

confidence: 99%

Consistency Of Definition Of Orthogonality In A Partial Metric Induced By A Metric

et al. 2023

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An extension of the metric space in which the distance of the same point is not always zero is called a partial metric space. Orthogonality is the relation of two perpendicular lines at one point of intersection forming a right angle. There are several ways to define orthogonality, including Pythagorean Orthogonality, Isosceles Orthogonality, and Birkhoff-James Orthogonality. The purpose of this research is to study the consistency of the definition of orthogonality in the metric space to the partial metric space. Based on these results, it can be concluded that the partial metric space can be obtained by linear induction from a metric space. Then, in developing the definition of orthogonality to the partial metric space, it can be concluded that the qualified orthogonality is the I-orthogonality and the BJ-orthogonality, while the P-orthogonality does not qualify the consistency of the definition of orthogonality in the partial metric space. Kata Kunci: Orthogonality, Consistency, and Partial metric space

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Compactness and completeness in partial metric spaces

Cited by 11 publications

References 16 publications

A Converse of the Banach Contraction Principle for Partial Metric Spaces and the Continuum Hypothesis

A Converse of the Banach Contraction Principle for Partial Metric Spaces and the Continuum Hypothesis

On Some Aspects of Compactness in Metric Spaces

Consistency Of Definition Of Orthogonality In A Partial Metric Induced By A Metric

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