## Gareth Fairey, Paul Gartside, Andrew Marsh

*Cardinal invariants of universals *

Comment.Math.Univ.Carolinae 46,4 (2005) 685-703. **Abstract:**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).

**Keywords:** zero set universals, continuous function universals, $S$ and $L$ spaces, admissible topology, cardinal invariants, function spaces

**AMS Subject Classification:** 54C30, 54C50, 54D65, 54D80, 54E35

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