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Soft super-continuity and soft delta-closed graphs
Dina Abuzaid1, Samer Al Ghour2, Monia Naghi1
1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
Plos One
|April 10, 2024
Summary
This study introduces soft super-continuity, a novel mapping concept in soft topology. It establishes soft super-continuity as a strong form of soft δ-continuity, distinct from soft continuity and soft complete continuity.
Area of Science:
- Topology
- Soft Topology
- Mathematical Analysis
Background:
- Soft topological spaces offer a framework for modeling uncertainty.
- Understanding new forms of continuity is crucial for advancing soft topology.
Purpose of the Study:
- To define and characterize a new concept: soft super-continuity.
- To explore its relationship with existing continuity concepts in soft topology.
Main Methods:
- Definition of soft super-continuity for soft mappings.
- Investigation of characterizations and properties.
- Comparative analysis with soft continuity, soft complete continuity, and soft δ-continuity.
Main Results:
- Soft super-continuity is introduced and characterized.
- It is shown to be strictly between soft continuity and soft complete continuity.
- Soft super-continuity is identified as a strong form of soft δ-continuity.
- Relationships with soft semi-regularity and soft δ-closed graphs are established.
Conclusions:
- Soft super-continuity offers a refined understanding of mappings in soft topological spaces.
- This concept provides a stronger form of soft δ-continuity.
- Further research can explore its applications and theoretical implications.
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