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1
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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.
2
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κ-strong sequences and the existence of generalized independent families

76%
Jureczko J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1277-1282
EN
In this paper we will show some relations between generalized versions of strong sequences introduced by Efimov in 1965 and independent families. We also show some inequalities between cardinal invariants associated with these both notions.
3
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κ-compactness, extent and the Lindelöf number in LOTS

76%
Buhagiar D., Chetcuti E., Weber H.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1249-1264
EN
We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.
4
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Sequential + separable vs sequentially separable and another variation on selective separability

64%
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.
5
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On minimal Hausdorff and minimal Urysohn functions

64%
Cammaroto F., Catalioto A., Porter J.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1242-1251
EN
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
6
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Cardinal invariants of paratopological groups

64%
Sánchez I.
Topological Algebra and its Applications
|
2013
|
tom 1
37-45
EN
We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.
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