Methodological remarks on soft topology

Matejdes, Milan

doi:10.1007/s00500-021-05587-7

Cited by 15 publications

(10 citation statements)

References 14 publications

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“…In -Soft topologies are point-set topologies on a product space (cf., [27]). Is there a comparable result for convex soft geometries?…”

Section: Discussionmentioning

confidence: 99%

Convex Soft Geometries

Alcantud

2022

JCCE

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This paper introduces convex soft geometries. The import of this model is that it extends a successful field of research, namely, convex geometries, to account for alternatives characterized by a multiplicity of attributes. Related concepts include soft convex hulls and a notion of extreme elements. Some fundamental results are proven. Among them, we guarantee that an anti-exchange property holds true. Importantly, the existence of extreme elements is guaranteed hence proving their suitability for applied studies. Both results are natural (but non-trivial) extensions of comparable outputs for convex geometries. We present a detailed research program that might stimulate future investigations on this new research area.

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“…In -Soft topologies are point-set topologies on a product space (cf., [27]). Is there a comparable result for convex soft geometries?…”

Section: Discussionmentioning

confidence: 99%

Convex Soft Geometries

Alcantud

2022

JCCE

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“…Definition 3.1. ( [1][2][3][4][5][6][7], [11][12][13][14][15][16][17][18][19][20][21]) Let E, U be two nonempty sets.…”

Section: Soft Topology and Topology On E × Uunclassified

“…This notation is more natural than that of (U, τ, E), because first the sets are given and then the structure on them. [11][12][13][14][15][16][17][18][19][20][21]) Let E, U be two nonempty sets.…”

Section: Definition 32 ([14]mentioning

confidence: 99%

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On some operations on soft topological spaces

Matejdes

2021

Filomat

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The aim of the article is to point out a one-to-one correspondence between soft topological spaces over a universe U with respect to a parameter set E and topological ones on the Cartesian product E x U. From this point of view, all soft topological terms, soft operations, soft functions and properties of soft topological spaces are actually topological concepts. Because the set valued mappings and set valued analysis have great application potential, it is necessary to look for their meaningful use with respect to standard topological methods and set valued analysis procedures.

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“…Çaǧman et al [10] used a soft set to demonstrate the notion of soft topological space. Following that, several academics concentrated on soft topological spaces [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Topological Structures via Bipolar Hypersoft Sets

Musa

Asaad

2022

Journal of Mathematics

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In this article, we introduce bipolar hypersoft topological spaces over the collection of bipolar hypersoft sets. It is proven that a bipolar hypersoft topological space gives a parametrized family of hypersoft topological spaces, but the converse does not hold in general, and this is shown with the help of an example. Furthermore, we give a condition on a given parametrized family of hypersoft topologies, which assure that there is a bipolar hypersoft topology whose induced family of hypersoft topologies is the given family. The notions of bipolar hypersoft neighborhood, bipolar hypersoft subspace, and bipolar hypersoft limit points are introduced. Finally, we define bipolar hypersoft interior, bipolar hypersoft closure, bipolar hypersoft exterior, and bipolar hypersoft boundary, and the relations between them, differing from the relations on hypersoft topology, are investigated.

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Methodological remarks on soft topology

Cited by 15 publications

References 14 publications

Convex Soft Geometries

Convex Soft Geometries

On some operations on soft topological spaces

Topological Structures via Bipolar Hypersoft Sets

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