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Cardinal invariants of universals

Gareth Fairey, Paul Gartside, Andrew Marsh (2005)

Commentationes Mathematicae Universitatis Carolinae

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 . 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...

Classifications and characterizations of Baire-1 functions

Persephone Kiriakouli (1998)

Commentationes Mathematicae Universitatis Carolinae

Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space K , to the subclasses 1 ξ ( K ) , ξ < ω 1 . In [8], for every ordinal ξ < ω 1 we define a new type of convergence for sequences of real-valued functions ( ξ -uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space K , and...

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