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The separation and compactness on fuzzy partial metric spaces.
Han Wang1, Chong Shen2,3, Zhenyu Jin4
1School of Mathematical Sciences, Nanjing Normal University, Jiangsu 210023, China.
Fundamental Research
|April 13, 2026
Summary
This study explores topological properties in fuzzy partial metric spaces (FPMS). Researchers found that certain separation axioms (T2, T3, T4) are equivalent in FPMS, and compactness is linked to being absolutely totally bounded and complete.
Area of Science:
- Topology
- Fuzzy Mathematics
- Metric Spaces
Background:
- Fuzzy partial metric spaces (FPMS) are an extension of metric spaces with applications in topology.
- Understanding topological properties is crucial for developing the theory of FPMS.
Purpose of the Study:
- To investigate separation axioms within FPMS.
- To introduce and analyze the concept of absolutely totally bounded FPMS.
- To establish conditions for compactness in FPMS.
Main Methods:
- Examination of separation axioms (T2, T3, T4) in the context of FPMS.
- Introduction and theoretical analysis of the 'absolutely totally bounded' property for FPMS.
- Proof of equivalence between compactness and the combination of absolute total boundedness and completeness in FPMS.
Main Results:
- Demonstration of the equivalence of T2, T3, and T4 separation axioms in FPMS under specific conditions.
- Introduction of the concept of absolutely totally bounded FPMS.
- Proof that a FPMS is compact if and only if it is both absolutely totally bounded and complete.
Conclusions:
- The study clarifies the relationships between separation axioms in FPMS.
- The findings provide a new characterization of compactness in FPMS using absolute total boundedness and completeness.
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