Remarks on quasi-metric spaces

Dũng, Nguyễn Văn

doi:10.18514/mmn.2014.1139

Cited by 6 publications

(2 citation statements)

References 12 publications

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“…Since then, several works have dealt with other theoretical field in such spaces, see [17], [18], [19], [11], [20], [21], [22], [23], [24], [25], [26], [27]and [28]. In 2017, Kamran and et al [29] introduced an extension of s-distance, where they expanded the triangle inequality by using the real-valued function 𝑑 𝜃 : :Ω…”

Section: Example (1) [10]mentioning

confidence: 99%

Survey about Generalizing Distances

Al-Bundi

2022

JAM

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As known, in general topology the talking be about “nearness”. This is exactly needed to discuss subjects such convergence and continuity. The simple way to study about nearness is to correspond the set with a distance function to inform us how far apart two elements of are. The metric concept introduced by a French mathematician Maurice René Fréchet (1878 – 1973) in 1906 in his work on some points of the functional calculus. However, the name is due to a German mathematician Felix Hausdorff (1868 –1942) who is considered to be one of the founders of modern topology. In addition to these contribution, he contributed significantly to set theory, descriptive set theory, measure theory, and functional analysis.

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Section: Example (1) [10]mentioning

confidence: 99%

Survey about Generalizing Distances

Al-Bundi

2022

JAM

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“…For the sake of self-containment of this note, we shall recollect some basic concepts of quasi-metric space. For more details, we refer the reader to [2][3][4]. (ω 1 ) ω(p, q) = 0 ⇔ p = q ; (ω 2 ) ω(p, s) ≤ ω(p, q) + ω(q, s), for all p, q, s ∈ M.…”

Section: Definitionmentioning

confidence: 99%