A generalization of a generic theorem in the theory of cardinal invariants of topological spaces

Alejandro Ramírez-Páramo; Noé Trinidad Tapia-Bonilla

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 177-187
  • ISSN: 0010-2628

Abstract

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The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If X is a T 2 -space, then | X | ≤ 2 L ( X ) χ ( X ) . Moreover, we will show relative versions of three well-known cardinal inequalities.

How to cite

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Ramírez-Páramo, Alejandro, and Tapia-Bonilla, Noé Trinidad. "A generalization of a generic theorem in the theory of cardinal invariants of topological spaces." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 177-187. <http://eudml.org/doc/250240>.

@article{Ramírez2007,
abstract = {The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If $X$ is a $T_2$-space, then $|X|\le 2^\{L(X)\chi (X)\}$. Moreover, we will show relative versions of three well-known cardinal inequalities.},
author = {Ramírez-Páramo, Alejandro, Tapia-Bonilla, Noé Trinidad},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cardinal functions; cardinal inequalities; cardinal function; cardinal inequality; closure operator},
language = {eng},
number = {1},
pages = {177-187},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A generalization of a generic theorem in the theory of cardinal invariants of topological spaces},
url = {http://eudml.org/doc/250240},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Ramírez-Páramo, Alejandro
AU - Tapia-Bonilla, Noé Trinidad
TI - A generalization of a generic theorem in the theory of cardinal invariants of topological spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 177
EP - 187
AB - The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If $X$ is a $T_2$-space, then $|X|\le 2^{L(X)\chi (X)}$. Moreover, we will show relative versions of three well-known cardinal inequalities.
LA - eng
KW - cardinal functions; cardinal inequalities; cardinal function; cardinal inequality; closure operator
UR - http://eudml.org/doc/250240
ER -

References

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  9. Hodel R.E., Combinatorial set theory and cardinal functions inequalities, Proc. Amer. Math. Soc. 111 (1992), 567-575. (1992) MR1039531
  10. Hodel R.E., Cardinal functions I, in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.1-61. Zbl0559.54003MR0776620
  11. Juhász I., Cardinal Functions in Topology - Ten Years Later, Mathematisch Centrum, Amsterdam, 1980. MR0576927
  12. Stavrova, D., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc. 25 (2000), 333-343. (2000) Zbl1027.54006MR1925691
  13. Shu-Hao S., Two new topological cardinal inequalities, Proc. Amer. Math. Soc. 104 (1988), 313-316. (1988) MR0958090

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