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Proceedings of the American Mathematical Society

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The cohesive property


Author: Gerald Jungck
Journal: Proc. Amer. Math. Soc. 84 (1982), 138-142
MSC: Primary 54E65
DOI: https://doi.org/10.1090/S0002-9939-1982-0633295-9
MathSciNet review: 633295
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Abstract: We introduce the concept of cohesive families of neighborhood bases. We thereby obtain conditions necessary and sufficient to ensure that a separable space be second countable, and sufficiency conditions for complete collectionwise normality. As by-products we obtain metrizability criteria. We prove, e.g., that a $ {T_1}$ space is metrizable iff it has a refined development $ \{ {G_n}:n \in N\} $ such that $ \{ {B_p}:p \in X\} $ with $ {B_p} = \{ {\text{St}}(p,{G_n}):n \in N\} $ is cohesive.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0633295-9
Keywords: Cohesive families, semimetric, developable, metrizable
Article copyright: © Copyright 1982 American Mathematical Society

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