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Soft C-continuity and soft almost C-continuity between soft topological spaces
1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan.
Heliyon
|June 2, 2023
Summary
This study introduces weaker forms of soft continuity, called soft c-continuity and soft nearly c-continuity. These new concepts are explored for their properties and applications in characterizing soft compactness in soft topological spaces.
Area of Science:
- Topology
- Set Theory
- Mathematical Analysis
Background:
- Existing research in soft topology focuses on concepts like soft continuity and soft almost continuity.
- There is a need for weaker forms of these concepts to provide more nuanced analysis of soft topological spaces.
- Understanding the behavior of functions under restrictions and compositions is crucial in topological studies.
Purpose of the Study:
- To introduce and define soft c-continuity and soft nearly c-continuity as weaker versions of existing soft topological concepts.
- To investigate the characterizations, properties, and preservation of these new notions under soft restrictions.
- To explore the composition of functions exhibiting these new continuity types and their implications for soft compactness.
Main Methods:
- Development of theoretical frameworks for soft c-continuity and soft nearly c-continuity.
- Utilizing soft restrictions to analyze the behavior of these new continuity types.
- Employing soft -open sets and soft regular open sets to characterize soft compactness and soft bases.
- Investigating the composition of soft continuous functions.
- Comparing novel soft topological notions with their general topological analogs.
Main Results:
- Several characterizations for soft c-continuity and soft nearly c-continuity are established.
- These new continuity concepts are shown to be preserved under soft restrictions.
- Conditions for the composition of soft c-continuous and soft nearly c-continuous functions are determined.
- A characterization of soft compactness using soft -open sets is provided.
- The collection of soft regular open sets with soft compact complements is shown to form a soft base for a coarser soft topology.
Conclusions:
- The study successfully introduces and analyzes novel weaker forms of continuity in soft topology.
- The findings contribute to a deeper understanding of soft topological spaces, particularly concerning compactness and function composition.
- The research highlights the relationships between soft topology and general topology, bridging theoretical gaps.
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