Reflecting character and pseudocharacter

Lucia R. Junqueira; Alberto M. E. Levi

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 3, page 365-376
  • ISSN: 0010-2628

Abstract

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We say that a cardinal function φ reflects an infinite cardinal κ , if given a topological space X with φ ( X ) ≥ κ , there exists Y ∈ [ X ] ≤ κ with φ ( Y ) ≥ κ . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with CH .

How to cite

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Junqueira, Lucia R., and Levi, Alberto M. E.. "Reflecting character and pseudocharacter." Commentationes Mathematicae Universitatis Carolinae 56.3 (2015): 365-376. <http://eudml.org/doc/271664>.

@article{Junqueira2015,
abstract = {We say that a cardinal function $\phi $ reflects an infinite cardinal $\kappa $, if given a topological space $X$ with $\phi (X) \ge \kappa $, there exists $Y\in [X]^\{\le \kappa \}$ with $\phi (Y)\ge \kappa $. We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with $\mathrm \{CH\}$.},
author = {Junqueira, Lucia R., Levi, Alberto M. E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cardinal function; character; pseudocharacter; reflection theorem; compact spaces; Lindelöf spaces; continuum hypothesis},
language = {eng},
number = {3},
pages = {365-376},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Reflecting character and pseudocharacter},
url = {http://eudml.org/doc/271664},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Junqueira, Lucia R.
AU - Levi, Alberto M. E.
TI - Reflecting character and pseudocharacter
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 3
SP - 365
EP - 376
AB - We say that a cardinal function $\phi $ reflects an infinite cardinal $\kappa $, if given a topological space $X$ with $\phi (X) \ge \kappa $, there exists $Y\in [X]^{\le \kappa }$ with $\phi (Y)\ge \kappa $. We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences with $\mathrm {CH}$.
LA - eng
KW - cardinal function; character; pseudocharacter; reflection theorem; compact spaces; Lindelöf spaces; continuum hypothesis
UR - http://eudml.org/doc/271664
ER -

References

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  14. Junqueira L.R., Tall F.D., 10.1016/S0166-8641(97)00075-8, Topology Appl. 82 (1998), 239–266. Zbl0903.54002MR1602479DOI10.1016/S0166-8641(97)00075-8
  15. Junqueira L.R., Upwards preservation by elementary submodels, Topology Proc. 25 (2000), 225–249. Zbl1002.54003MR1875594
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