# Covering ${}^{\omega}\omega $ by special Cantor sets

Commentationes Mathematicae Universitatis Carolinae (2002)

- Volume: 43, Issue: 3, page 497-509
- ISSN: 0010-2628

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topGruenhage, Gary, and Levy, Ronnie. "Covering $^\omega \omega $ by special Cantor sets." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 497-509. <http://eudml.org/doc/22649>.

@article{Gruenhage2002,

abstract = {This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space $^\omega \omega $ of irrationals, or certain of its subspaces. In particular, given $f\in \{\}^\omega (\omega \setminus \lbrace 0\rbrace )$, we consider compact sets of the form $\prod _\{i\in \omega \}B_i$, where $|B_i|= f(i)$ for all, or for infinitely many, $i$. We also consider “$n$-splitting” compact sets, i.e., compact sets $K$ such that for any $f\in K$ and $i\in \omega $, $|\lbrace g(i):g\in K, g\upharpoonright i=f\upharpoonright i\rbrace |= n$.},

author = {Gruenhage, Gary, Levy, Ronnie},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {irrationals; $f$-cone; weak $f$-cone; $n$-splitting compact set; irrationals; -cone; -splitting compact set},

language = {eng},

number = {3},

pages = {497-509},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Covering $^\omega \omega $ by special Cantor sets},

url = {http://eudml.org/doc/22649},

volume = {43},

year = {2002},

}

TY - JOUR

AU - Gruenhage, Gary

AU - Levy, Ronnie

TI - Covering $^\omega \omega $ by special Cantor sets

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2002

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 43

IS - 3

SP - 497

EP - 509

AB - This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space $^\omega \omega $ of irrationals, or certain of its subspaces. In particular, given $f\in {}^\omega (\omega \setminus \lbrace 0\rbrace )$, we consider compact sets of the form $\prod _{i\in \omega }B_i$, where $|B_i|= f(i)$ for all, or for infinitely many, $i$. We also consider “$n$-splitting” compact sets, i.e., compact sets $K$ such that for any $f\in K$ and $i\in \omega $, $|\lbrace g(i):g\in K, g\upharpoonright i=f\upharpoonright i\rbrace |= n$.

LA - eng

KW - irrationals; $f$-cone; weak $f$-cone; $n$-splitting compact set; irrationals; -cone; -splitting compact set

UR - http://eudml.org/doc/22649

ER -

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