Journal Article10.2298/fil2309845r
Soft expandable spaces
Amani Rawshdeh,Heyam H. Al-Jarrah,Tareq M. Al-shami +2 more
- Filomat
15
TL;DR: Soft expandable spaces are a generalization of soft paracompact and countably soft compact spaces. They have properties equivalent to soft LF soft open refinement and soft paracompactness under certain conditions.
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Abstract: In this study, we first introduce a new class of spaces, namely soft
expandable spaces, which is a generalization of soft paracompact and
countably soft compact spaces. Some properties of these spaces that are
discussed in this paper the soft expandable space is equivalent to every
A?-soft cover has softLF soft open refinement. Also, we discuss under what
conditions that countably soft expandable space is soft paracompact. With
the help of interesting examples, we elucidate there is no relationship
between soft topology and its parametric topologies with respect to
possession the property of being a soft expandable space. In this regards,
we discuss the role of extended soft topology to inherited this property to
classical topology. Second, we define the concept of s-expandable spaces
which is stronger than soft expandable spaces. We give some
characterizations of this concept, and investigate some equivalent concepts
to sexpandable spaces. In the end, we study the behaviours of soft
s-expandable spaces under some types of soft mappings.
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Citations
A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies
TL;DR: Weakly soft semi-open subsets as mentioned in this paper are a new class of generalizations of soft open sets, inspired by the components of a soft set, which can be used to reformulate existing soft topological concepts and examine their behaviors.
35
A weak form of soft $ \alpha $-open sets and its applications via soft topologies
TL;DR: In this paper , the concept of weakly soft $ \alpha $-open subsets and its relation to soft open sets are discussed. And the authors introduce the interior and closure operators inspired by the classes of soft subsets, and derive some formulas that describe the relations among them.
21
On weakly soft β-open sets and weakly soft β-continuity
Tareq M. Al-shami,M. M. Arar,Radwan Abu-Gdairi,Zanyar A. Ameen +3 more
- 28 Jul 2023
TL;DR: This paper introduces weakly soft β-open sets, expanding soft topology to a new soft structure, and explores connections with other classes via soft topology, relationships under extended and hyperconnected topologies, and characterizations of weakly soft β-continuous functions.
8
On soft parametric somewhat-open sets and applications via soft topologies
TL;DR: This work introduces soft parametric somewhat-open sets, exploring their features and cardinality bounds, and derives novel soft compact and Lindelöf spaces, examining their relations and navigation between soft and parametric structures.
6
On weakly soft somewhat open sets
Tareq M. Al-shami,Abdelwaheb Mhemdi,Amani Rawshdeh,Heyam H. Al-Jarrah +3 more
TL;DR: This paper introduces weakly soft somewhat open sets, a generalization of soft open sets, and explores their properties, including new soft operators and categories of soft mappings, with a focus on parametric topologies and their connections to soft topology.
5
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