On the cardinality of Urysohn spaces and weakly H -closed spaces

Fortunata Aurora Basile; Nathan Carlson

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 3, page 325-336
  • ISSN: 0862-7959

Abstract

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We introduce the cardinal invariant θ - a L ' ( X ) , related to θ - a L ( X ) , and show that if X is Urysohn, then | X | ≤ 2 θ - a L ' ( X ) χ ( X ) . As θ - a L ' ( X ) ≤ a L ( X ) , this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly H -closed spaces, related to H -closed spaces.

How to cite

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Basile, Fortunata Aurora, and Carlson, Nathan. "On the cardinality of Urysohn spaces and weakly $H$-closed spaces." Mathematica Bohemica 144.3 (2019): 325-336. <http://eudml.org/doc/294829>.

@article{Basile2019,
abstract = {We introduce the cardinal invariant $\theta $-$aL^\{\prime \}(X)$, related to $\theta $-$aL(X)$, and show that if $X$ is Urysohn, then $|X|\le 2^\{\theta \text\{-\}aL^\{\prime \}(X)\chi (X)\}$. As $\theta $-$aL^\{\prime \}(X)\le aL(X)$, this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly $H$-closed spaces, related to $H$-closed spaces.},
author = {Basile, Fortunata Aurora, Carlson, Nathan},
journal = {Mathematica Bohemica},
keywords = {Urysohn space; $\theta $-closure; pseudocharacter; almost Lindelöf degree; cardinality; cardinal invariant},
language = {eng},
number = {3},
pages = {325-336},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the cardinality of Urysohn spaces and weakly $H$-closed spaces},
url = {http://eudml.org/doc/294829},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Basile, Fortunata Aurora
AU - Carlson, Nathan
TI - On the cardinality of Urysohn spaces and weakly $H$-closed spaces
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 3
SP - 325
EP - 336
AB - We introduce the cardinal invariant $\theta $-$aL^{\prime }(X)$, related to $\theta $-$aL(X)$, and show that if $X$ is Urysohn, then $|X|\le 2^{\theta \text{-}aL^{\prime }(X)\chi (X)}$. As $\theta $-$aL^{\prime }(X)\le aL(X)$, this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly $H$-closed spaces, related to $H$-closed spaces.
LA - eng
KW - Urysohn space; $\theta $-closure; pseudocharacter; almost Lindelöf degree; cardinality; cardinal invariant
UR - http://eudml.org/doc/294829
ER -

References

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  10. Kočinac, L. D., On the cardinality of Urysohn and H -closed spaces, Proc. Math. Conf., Priština, 1994 Univ. of Priština, Faculty of Sciences, Priština (1995), L. D. Kočinac 105-111. (1995) Zbl0877.54002MR1466279
  11. Kočinac, L. D., On the cardinality of Urysohn spaces, Questions and Answers in General Topology 13 (1995), 211-216. (1995) Zbl0838.54002MR1350238
  12. Porter, J. R., Woods, R. G., 10.1007/978-1-4612-3712-9, Springer, New York (1988). (1988) Zbl0652.54016MR0918341DOI10.1007/978-1-4612-3712-9
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