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Baire classes of affine vector-valued functions

Ondřej F. K. Kalenda, Jiří Spurný (2016)

Studia Mathematica

We investigate Baire classes of strongly affine mappings with values in Fréchet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of L₁-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the...

Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

We characterize Baire-like spaces Cc(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.

Baire-one mappings contained in a usco map

Ondřej F. K. Kalenda (2007)

Commentationes Mathematicae Universitatis Carolinae

We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in ℝ d is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.

Banach spaces of bounded Szlenk index

E. Odell, Th. Schlumprecht, A. Zsák (2007)

Studia Mathematica

For a countable ordinal α we denote by α the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each α admits a separable, reflexive universal space. We also show that spaces in the class ω α · ω embed into spaces of the same class with a basis. As a consequence we deduce that each α is analytic in the Effros-Borel structure of subspaces of C[0,1].

Banach spaces of bounded Szlenk index II

D. Freeman, E. Odell, Th. Schlumprecht, A. Zsák (2009)

Fundamenta Mathematicae

For every α < ω₁ we establish the existence of a separable Banach space whose Szlenk index is ω α ω + 1 and which is universal for all separable Banach spaces whose Szlenk index does not exceed ω α ω . In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with Tsirelson type upper estimates.

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