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On some generated soft topological spaces and soft homogeneity
Samer Al Ghour1, Awatef Bin-Saadon1
1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan.
Heliyon
|July 25, 2019
Summary
This study introduces soft homogeneity, extending homogeneity concepts in topological spaces. Researchers explored soft minimal open sets and homogeneity relations within generated soft topologies, presenting new findings and examples.
Area of Science:
- Topology
- General Mathematics
Background:
- Homogeneity is a key concept in topological spaces.
- Existing research on soft topology has limitations in exploring homogeneity.
Purpose of the Study:
- To introduce and define soft homogeneity as an extension of homogeneity.
- To investigate soft minimal open sets within soft topologies.
- To analyze the homogeneity relation between soft and classical topologies.
Main Methods:
- Generating a soft topology from an indexed family of classical topologies.
- Applying concepts of soft minimal open sets.
- Examining the homogeneity relation.
Main Results:
- Introduction of soft homogeneity.
- Identification of soft minimal open sets.
- Establishment of homogeneity relations and associated results.
- Presentation of illustrative examples and counterexamples.
Conclusions:
- Soft homogeneity provides a novel extension to homogeneity in topological spaces.
- The study deepens the understanding of soft minimal open sets and homogeneity relations in soft topology.
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