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Keywords:
zero set universals; continuous function universals; $S$ and $L$ spaces; admissible topology; cardinal invariants; function spaces
zero set universals; continuous function universals; $S$ and $L$ spaces; admissible topology; cardinal invariants; function spaces
Summary:
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).
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