A lattice of conditions on topological spaces

Collins, P. J.; Reed, G. M.; Roscoe, A. W.; Rudin, M. E.

doi:10.1090/S0002-9939-1985-0787900-X

A lattice of conditions on topological spaces
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by P. J. Collins, G. M. Reed, A. W. Roscoe and M. E. Rudin PDF

Proc. Amer. Math. Soc. 94 (1985), 487-496 Request permission

Abstract:

If $W(x)$ (for each $x \in X$) is a family of subsets each containing $x$, various conditions on $\left \{ {W(x):x \in X} \right \}$ are investigated. They yield new criteria for paracompactness, metrisability and the existence of a semimetric generating a given topology.

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