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Generalized metric spaces and topological structure I. (English) Zbl 0995.54020
Summary: Some results in $$D$$-metric spaces are obtained and the notion of open and closed balls is introduced. The $$D$$-metric topology is defined which is further studied for its topological properties, completeness and compactness properties of $$D$$-metric spaces.

##### MSC:
 54E35 Metric spaces, metrizability 54B10 Product spaces in general topology 54C05 Continuous maps 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54E45 Compact (locally compact) metric spaces