Geodesic
Cardinal invariants of universals
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 4, pp. 685-703 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We examine when a space $X$ has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the $\sigma$-weight of $X$ when $X$ is perfectly normal. We also show that if $Y$ parametrises a zero set universal for $X$ then $hL(X^n)\leq hd(Y)$ for all $n\in \Bbb N$. We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a $K$-coarser topology. Examples are given including an $S$ space with zero set universal parametrised by an $L$ space (and vice versa).
We examine when a space $X$ has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the $\sigma$-weight of $X$ when $X$ is perfectly normal. We also show that if $Y$ parametrises a zero set universal for $X$ then $hL(X^n)\leq hd(Y)$ for all $n\in \Bbb N$. We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a $K$-coarser topology. Examples are given including an $S$ space with zero set universal parametrised by an $L$ space (and vice versa).
Classification : 54A25, 54C30, 54C50, 54D65, 54D80, 54E35
Keywords: zero set universals; continuous function universals; $S$ and $L$ spaces; admissible topology; cardinal invariants; function spaces 
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     author = {Fairey, Gareth and Gartside, Paul and Marsh, Andrew},
     title = {Cardinal invariants of universals},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {685--703},
     year = {2005},
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Fairey, Gareth; Gartside, Paul; Marsh, Andrew. Cardinal invariants of universals. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 4, pp. 685-703. http://geodesic.mathdoc.fr/item/CMUC_2005_46_4_a7/