Covering ω ω by special Cantor sets

Gary Gruenhage; Ronnie Levy

Commentationes Mathematicae Universitatis Carolinae (2002)

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

Abstract

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This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω ω of irrationals, or certain of its subspaces. In particular, given f ∈ ω ( ω ∖ { 0 } ) , we consider compact sets of the form ∏ i ∈ ω 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 ∈ K and i ∈ ω , | { g ( i ) : g ∈ K , g ↾ i = f ↾ i } | = n .

How to cite

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Gruenhage, 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 -

References

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