Geodesic
Covering $^\omega\omega$ by special Cantor sets
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 497-509

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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 $f\in {}^\omega (\omega \setminus \{0\})$, 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 $, $|\{g(i):g\in K, g\restriction i=f\restriction i\}|= n$.
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 $f\in {}^\omega (\omega \setminus \{0\})$, 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 $, $|\{g(i):g\in K, g\restriction i=f\restriction i\}|= n$.
Classification : 03E17, 03E35, 54A35
Keywords: irrationals; $f$-cone; weak $f$-cone; $n$-splitting compact set 
Gruenhage, Gary; Levy, Ronnie. Covering $^\omega\omega$ by special Cantor sets. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 497-509. http://geodesic.mathdoc.fr/item/CMUC_2002_43_3_a9/
@article{CMUC_2002_43_3_a9,
     author = {Gruenhage, Gary and Levy, Ronnie},
     title = {Covering $^\omega\omega$ by special {Cantor} sets},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {497--509},
     year = {2002},
     volume = {43},
     number = {3},
     mrnumber = {1920525},
     zbl = {1072.03028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002_43_3_a9/}
}
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