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On soft parametric somewhat-open sets and applications via soft topologies
Tareq M Al-Shami1, Abdelwaheb Mhemdi2
1Department of Mathematics, Sana'a University, Sana'a, Yemen.
Heliyon
|November 15, 2023
Summary
This study introduces soft parametric somewhat-open sets in topological spaces, extending existing concepts. These new sets aid in defining novel soft compact and Lindelöf spaces and understanding connectivity properties.
Area of Science:
- Topology
- Set Theory
- Mathematical Analysis
Background:
- General topology and soft set theory are foundational mathematical fields.
- Existing research explores generalizations of open sets and their topological properties.
- Parametric topological spaces offer a framework for studying topological structures with parameters.
Purpose of the Study:
- To introduce and investigate a new class of soft sets called soft parametric somewhat-open sets.
- To define and analyze novel soft compact and soft Lindelöf spaces based on these new sets.
- To explore the concept of soft ps-connected spaces and their relationship with existing topological properties.
Main Methods:
- Definition and exploration of the basic properties of soft parametric somewhat-open sets.
- Derivation of formulas for the bounds of the cardinality of these sets.
- Introduction of new types of soft compact and soft Lindelöf spaces and examination of their relationships.
- Investigation of soft ps-connected spaces and their equivalences.
Main Results:
- Soft parametric somewhat-open sets are defined as a proper extension of soft open and soft somewhat-open sets.
- Formulas are derived to determine the bounds of the cardinality of soft parametric somewhat-open subsets.
- New characterizations of soft compact and soft Lindelöf spaces are established.
- The concept of soft ps-connected spaces is introduced and shown to be equivalent to soft hyperconnected spaces.
Conclusions:
- The introduced soft parametric somewhat-open sets provide a novel framework for studying topological spaces.
- The new classes of soft compact and soft Lindelöf spaces offer deeper insights into topological structures.
- The study establishes important connections between parametric topology, soft sets, and connectivity properties.
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