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Monotone weak Lindelöfness

100%
Bonanzinga M., Cammaroto F., Pansera B.
Open Mathematics
|
2011
|
tom 9
|
nr 3
583-592
EN
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.
2
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Sequential + separable vs sequentially separable and another variation on selective separability

100%
Bella A., Bonanzinga M., Matveev M.
Open Mathematics
|
2013
|
tom 11
|
nr 3
530-538
EN
A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.
3
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On the cardinality of n-Urysohn and n-Hausdorff spaces

100%
Bonanzinga M., Cuzzupé M., Pansera B.
Open Mathematics
|
2014
|
tom 12
|
nr 2
330-336
EN
Two variations of Arhangelskii’s inequality $$\left| X \right| \leqslant 2^{\chi (X) - L(X)}$$ for Hausdorff X [Arhangel’skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967–970 (in Russian)] given in [Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343] are extended to the classes with finite Urysohn number or finite Hausdorff number.
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