The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪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 Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed. © 2011 Versita Warsaw and Springer-Verlag Wien.
Monotone weak Lindelöfness / Bonanzinga, M.; Cammaroto, F.; Pansera, B. A.. - In: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 1895-1074. - 9:3(2011), pp. 583-592. [10.2478/s11533-011-0025-z]
Monotone weak Lindelöfness
Pansera B. A.
2011-01-01
Abstract
The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪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 Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed. © 2011 Versita Warsaw and Springer-Verlag Wien.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
