Cardinal invariants of universals

Gareth Fairey; Paul Gartside; Andrew Marsh

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 4, page 685-703
  • ISSN: 0010-2628

Abstract

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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 σ -weight of X when X is perfectly normal. We also show that if Y parametrises a zero set universal for X then h L ( X n ) ≤ h d ( Y ) for all n ∈ 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).

How to cite

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Fairey, Gareth, Gartside, Paul, and Marsh, Andrew. "Cardinal invariants of universals." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 685-703. <http://eudml.org/doc/249556>.

@article{Fairey2005,
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 $hL(X^n)\le hd(Y)$ for all $n\in \mathbb \{N\}$. 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).},
author = {Fairey, Gareth, Gartside, Paul, Marsh, Andrew},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {zero set universals; continuous function universals; $S$ and $L$ spaces; admissible topology; cardinal invariants; function spaces; zero set universals; continuous function universals; and spaces; admissible topology},
language = {eng},
number = {4},
pages = {685-703},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Cardinal invariants of universals},
url = {http://eudml.org/doc/249556},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Fairey, Gareth
AU - Gartside, Paul
AU - Marsh, Andrew
TI - Cardinal invariants of universals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 685
EP - 703
AB - 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 $hL(X^n)\le hd(Y)$ for all $n\in \mathbb {N}$. 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).
LA - eng
KW - zero set universals; continuous function universals; $S$ and $L$ spaces; admissible topology; cardinal invariants; function spaces; zero set universals; continuous function universals; and spaces; admissible topology
UR - http://eudml.org/doc/249556
ER -

References

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