Soft topological space and topology on the Cartesian product

Matejdes, Milan

doi:10.15672/hjms.20164513117

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…Let us review the literature that examined the topology and different methods of constructing soft topology. In [13], Milan conducted the study on soft topological space, exploring their connection with a topological space defined on the Cartesian product of two sets through a homeomorphism. In 2019, Terepeta [14] discussed a method of constructing a soft topology from any ordinary topology on a nonempty set V while considering any possible set of parameters.…”

Section: Literature Review Of Studies Of Constructing Soft Topologymentioning

confidence: 99%

Innovative Strategy for Constructing Soft Topology

Alajlan,

Alghamdi

2023

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To address the complexity of daily problems, soft set theory has emerged as a valuable tool, providing innovative mathematical techniques to manage vast amounts of data and ambiguity. The study of soft topology involves the investigation of various properties of soft sets and functions, as well as the development of new mathematical models and techniques for addressing uncertainty. The main motivation of this paper is to delve deeper into the subject and devise new methodologies to address real-world challenges more effectively and unlock the full potential of soft sets in various applications. In this paper, we present a novel soft topology, which is constructed using soft single points on a nonempty set V in relation to a topology on V. We investigate and study the behaviors and properties associated with this particular type of soft topology. Furthermore, we shed light on the soft separation axioms with this type of soft topology and investigate whether these axioms are inherited from the corresponding ordinary topology or not. Our study is concerned with examining the connection between ordinary topologies and the soft topologies generated that arise from them, with the aim of identifying their interdependencies and potential implications. By studying the connection between soft topologies and their corresponding ordinary topologies, researchers are able to gain a deeper understanding of the properties and behaviors of these structures and develop new modeling approaches for dealing with uncertainty and complexity in data.

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Section: Literature Review Of Studies Of Constructing Soft Topologymentioning

confidence: 99%

Innovative Strategy for Constructing Soft Topology

Alajlan,

Alghamdi

2023

Axioms

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“…Lemma 2.9(Matejdes (2016);Matejdes (2021)) Let 𝐺𝑟(𝐹) = {(𝛼, 𝑥) ∈ 𝛺 × 𝑋: 𝑥 ∈ 𝐹(𝛼)}, which is the graph of the set-valued function 𝐹: 𝛺 → 𝒫(𝑋). Then 1.…”

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confidence: 99%

Minimal Soft Topologies

Ameen

Ghour

2022

New Math. and Nat. Computation

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A collection of all soft topologies over a fixed universe forms a complete lattice. One might ask: what will be the structure of minimal or maximal topologies in this lattice concerning specific topological properties? We know that the soft discrete topology is maximal soft [Formula: see text]-spaces, for [Formula: see text], in terms of the given soft point theory. As a result, we find it interesting to study the construction of minimal soft [Formula: see text] topologies. We show that the minimal soft [Formula: see text] is a nested soft topology whose base is the complements of all soft point closures. The minimal soft [Formula: see text] is the cofinite soft topology. The minimal soft [Formula: see text] (respectively, [Formula: see text]) is a soft topology in which each soft open (respectively, soft regular) filter base has only one adherent soft point and is convergent. Finally, the minimal soft [Formula: see text] topologies are subclasses of soft compact topologies.

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Soft ideal topological spaces

Matejdes

2021

Preprint

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Soft topological space and topology on the Cartesian product

Cited by 4 publications

References 18 publications

Innovative Strategy for Constructing Soft Topology

Innovative Strategy for Constructing Soft Topology

Minimal Soft Topologies

Soft ideal topological spaces

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