A study of a new dimension for frames

Georgiou, D.N.; Kougias, Ioannis; Megaritis, A.C.; Prinos, G.A.; Sereti, F.

doi:10.1016/j.topol.2019.106995

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…The proofs of the following propositions are similar to the proofs of Proposition 6, and Propositions 4.5 and 4.6 in [31].…”

Section: Definition 7 ([30]mentioning

confidence: 73%

“…It is commonly accepted that the notion of convergence is a fundamental topic in topology; moreover, topology and net convergence are characterized by each other, by using the so-called notion of net convergence class in [20] (the analogous characterization for fuzzy topology is given in [28]). In this paper, we insert the notion of fuzzy function ideal convergence as a natural generalization of both fuzzy net convergence in [26] and fuzzy net ideal convergence in [30,31] and provide a characterization of fuzzy topology via the notion of fuzzy function ideal convergence class. Specifically, we examine the necessary and sufficient conditions that a fuzzy function ideal convergence class L, on a non-empty set X, should fulfill to determine a unique fuzzy topology δ on X such that I-convergence (L) coincides with I-convergence, with respect to δ.…”

Section: Discussionmentioning

confidence: 99%

“…Afsan in [30]. Moreover, the authors of [31], by using the previous notion, obtained a modification of the Y.M. Liu characterization theorem on fuzzy convergence classes.…”

Section: Introductionmentioning

confidence: 99%

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A New Notion of Fuzzy Function Ideal Convergence

Georgiou,

Prinos

2024

Mathematics

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P.M. Pu and Y.M. Liu extended Moore-Smith’s convergence of nets to fuzzy topology and Y.M. Liu provided analogous results to J. Kelley’s classical characterization theorem of net convergence by introducing the notion of fuzzy convergence classes. In a previous paper, the authors of this study provided modified versions of this characterization by using an alternative notion of convergence of fuzzy nets, introduced by B.M.U. Afsan, named fuzzy net ideal convergence. Our main scope here is to generalize and simplify the preceding results. Specifically, we insert the concept of a fuzzy function ideal convergence class, L, on a non-empty set, X, consisting of triads (f,e,I), where f is a function from a non-empty set, D, to the set FP(X) of fuzzy points in X, which we call fuzzy function, e∈FP(X), and I is a proper ideal on D, and we provide necessary and sufficient conditions to establish the existence of a unique fuzzy topology, δ, on X, such that (f,e,I)∈L iff fI-converges to e, relative to the fuzzy topology δ.

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“…The proofs of the following propositions are similar to the proofs of Proposition 6, and Propositions 4.5 and 4.6 in [31].…”

Section: Definition 7 ([30]mentioning

confidence: 73%

Section: Discussionmentioning

confidence: 99%