The definition of monotone weak Lindelofness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelof if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) a(a)r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelof spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed.
Monotone weak Lindelofness
BONANZINGA, Maddalena;CAMMAROTO, Filippo;PANSERA, BRUNO ANTONIO
2011-01-01
Abstract
The definition of monotone weak Lindelofness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelof if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) a(a)r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelof spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed.File in questo prodotto:
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