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- W2908447342 abstract "Let ${text {c}}{{text {l}}_u}(A)$ be the $u$-closure of a subset $A$ of a space. We prove that a space is compact if and only if for each upper-semicontinuous multifunction $lambda$ on the space, the multifunction $mu$ defined on the space by $mu (x) = {text {c}}{{text {l}}_u}(lambda (x))$ assumes a maximal value under set inclusion. We also prove that in a Urysohn-closed space any two subsets with disjoint $u$-closures are separated by disjoint open subsets. The quotient space induced by identifying those points with identical $u$-closures is investigated and shown to be ${T_0}$." @default.
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- W2908447342 date "1981-01-01" @default.
- W2908447342 modified "2023-10-18" @default.
- W2908447342 title "Applications of the $u$-closure operator" @default.
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- W2908447342 doi "https://doi.org/10.1090/s0002-9939-1981-0620006-5" @default.
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