Separability and minimal weak base topologies

Davis, S. W.; Stephenson, R. M.

doi:10.1090/S0002-9939-1979-0524320-4

Separability and minimal weak base topologies
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by S. W. Davis and R. M. Stephenson

Proc. Amer. Math. Soc. 74 (1979), 371-378

DOI: https://doi.org/10.1090/S0002-9939-1979-0524320-4

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Abstract:

In this note, we present filter characterizations of minimal weakly first countable, minimal $\mathcal {F}$, minimal ${\mathcal {F}_r}$, weakly first countable-closed, $\mathcal {F}$-closed, and ${\mathcal {F}_r}$-closed spaces. Our main result is a generalization of G. M. Reed’s theorem that every Moore-closed space is separable.

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