Two cardinal inequalities for functionally Hausdorff spaces

Alessandro Fedeli

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 365-369
  • ISSN: 0010-2628

Abstract

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In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τ θ -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if X is a functionally Hausdorff space, then | X | ≤ 2 χ ( X ) wcd ( X ) .

How to cite

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Fedeli, Alessandro. "Two cardinal inequalities for functionally Hausdorff spaces." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 365-369. <http://eudml.org/doc/247614>.

@article{Fedeli1994,
abstract = {In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the $\tau \theta $-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if $X$ is a functionally Hausdorff space, then $|X|\le 2^\{\chi (X)\text\{\it wcd\}(X)\}$.},
author = {Fedeli, Alessandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cardinal functions; $\tau \theta $-closed sets; $w$-compactness degree; -closed sets; -compactness degree; cardinal inequalities},
language = {eng},
number = {2},
pages = {365-369},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Two cardinal inequalities for functionally Hausdorff spaces},
url = {http://eudml.org/doc/247614},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Fedeli, Alessandro
TI - Two cardinal inequalities for functionally Hausdorff spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 365
EP - 369
AB - In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the $\tau \theta $-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if $X$ is a functionally Hausdorff space, then $|X|\le 2^{\chi (X)\text{\it wcd}(X)}$.
LA - eng
KW - cardinal functions; $\tau \theta $-closed sets; $w$-compactness degree; -closed sets; -compactness degree; cardinal inequalities
UR - http://eudml.org/doc/247614
ER -

References

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  5. Ishii T., On the Tychonoff functor and w -compactness, Topology Appl. 11 (1980), 173-187. (1980) Zbl0441.54012MR0572372
  6. Pol R., Short proofs of two theorems on cardinality of topological spaces, Bull. Acad. Polon. Sci. Ser,. Math. Astr. Phys. 22 (1974), 1245-1249. (1974) Zbl0295.54004MR0383333
  7. Stephenson R.M., Jr., Spaces for which the Stone-Weierstrass theorem holds, Trans. Amer. Math. Soc. 133 (1968), 537-546. (1968) Zbl0164.53003MR0227753
  8. Stephenson R.M., Jr., Product spaces for which the Stone-Weierstrass theorem holds, Proc. Amer. Math. Soc. 21 (1969), 284-288. (1969) MR0250260
  9. Stephenson R.M., Jr., Pseudocompact and Stone-Weierstrass product spaces, Pacific J. Math. 99 (1) (1982), 159-174. (1982) Zbl0426.54009MR0651493

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