On the cardinality of n-Urysohn and n-Hausdorff spaces

Maddalena Bonanzinga; Maria Cuzzupé; Bruno Pansera

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 330-336
  • ISSN: 2391-5455

Abstract

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Two variations of Arhangelskii’s inequality X ⩽ 2 χ ( 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.

How to cite

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Maddalena Bonanzinga, Maria Cuzzupé, and Bruno Pansera. "On the cardinality of n-Urysohn and n-Hausdorff spaces." Open Mathematics 12.2 (2014): 330-336. <http://eudml.org/doc/269388>.

@article{MaddalenaBonanzinga2014,
abstract = {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.},
author = {Maddalena Bonanzinga, Maria Cuzzupé, Bruno Pansera},
journal = {Open Mathematics},
keywords = {Urysohn number of a space; Hausdorff number of a space; \[cl^\mathcal \{H\}\] -operator; θ-closure; \[cl\_\theta ^\mathcal \{H\}\] -operator; Relative Lindelöf number; Almost Lindelöf degree of a space; Urysohn number of space; Hausdorff number of space; relative Lindelöf number; almost Lindelöf degree of a space; -Urysohn pseudocharacter; -Hausdorff pseudocharacter},
language = {eng},
number = {2},
pages = {330-336},
title = {On the cardinality of n-Urysohn and n-Hausdorff spaces},
url = {http://eudml.org/doc/269388},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Maddalena Bonanzinga
AU - Maria Cuzzupé
AU - Bruno Pansera
TI - On the cardinality of n-Urysohn and n-Hausdorff spaces
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 330
EP - 336
AB - 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.
LA - eng
KW - Urysohn number of a space; Hausdorff number of a space; \[cl^\mathcal {H}\] -operator; θ-closure; \[cl_\theta ^\mathcal {H}\] -operator; Relative Lindelöf number; Almost Lindelöf degree of a space; Urysohn number of space; Hausdorff number of space; relative Lindelöf number; almost Lindelöf degree of a space; -Urysohn pseudocharacter; -Hausdorff pseudocharacter
UR - http://eudml.org/doc/269388
ER -

References

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  17. [17] Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343 Zbl1027.54006
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