4 papers
Generalizations of Chainability and Compactness, and the Hypertopologies
Ajit Kumar Gupta, Saikat Mukherjee
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 i…
Lebesgue Number and Total Boundedness
Ajit Kumar Gupta, Saikat Mukherjee
A generalization of the Lebesgue number lemma is obtained. It is proved that, if each countably infinite locally finite open cover of a chainable metric space has a Lebesgue nu…
Menger Convexity and Fixed Point Results
Ajit Kumar Gupta, Saikat Mukherjee
Shimizu and Takahashi proved that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty interse…
On Nonempty Intersection Properties in Metric Spaces
Ajit K. Gupta, Saikat Mukherjee
The classical Cantor's intersection theorem states that in a complete metric space , intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter…