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- W4281568301 abstract "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 $X$ has a Lebesgue number, then $X$ is totally bounded. A property of metric spaces which is a generalization of connectedness and Menger convexity is introduced. It is observed that Atsujiness and compactness are equivalent for a metric space with this introduced property as well as for a chainable metric space." @default.
- W4281568301 created "2022-05-27" @default.
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- W4281568301 date "2022-05-24" @default.
- W4281568301 modified "2023-09-24" @default.
- W4281568301 title "Lebesgue Number and Total Boundedness" @default.
- W4281568301 doi "https://doi.org/10.48550/arxiv.2205.11855" @default.
- W4281568301 hasPublicationYear "2022" @default.
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