Generalizations of Chainability and Compactness, and the Hypertopologies

Ajit Kumar Gupta; Saikat Mukherjee

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arXiv · 2301.07338

Generalizations of Chainability and Compactness, and the Hypertopologies

Ajit Kumar Gupta·Saikat Mukherjee

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Abstract

We study two properties for subsets of a metric space. One of them is generalization of chainability, finite chainability, and Menger convexity for metric spaces; while the other is a generalization of compactness. We explore the basic results related to these two properties. Further, in the perspective of these properties, we explore relations among the Hausdorff, Vietoris, and locally finite hypertopologies.

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BibTeX RIS

Ajit Kumar Gupta, Saikat Mukherjee. 2023-01-18. Generalizations of Chainability and Compactness, and the Hypertopologies. https://arxiv.org/abs/2301.07338

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