Baire sets and uniformities on complete metric spaces
Baire sets which are Borelian subspaces
Baire spaces and some generalizations of complete metric spaces
Baire spaces and weak topologies generated by gap and excess functionals
Baire spaces, -spaces, and some properly hereditary properties.
Baire-like spaces C(X,E)
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 for ordered
We show that if is a subspace of a linearly ordered space, then is a Baire space if and only if is Choquet iff has the Moving Off Property.
Baire-one mappings contained in a usco map
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 is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.
Baire's Space of Permutations of n and Rearrangements of Series
Ball versus distance convexity of metric spaces.
Banach algebras with involution
Banach Lattices with Locally Compact Representation Spaces.
Banach space valued mappings of the first Baire class contained in usco mappings
We prove that any Baire-one usco-bounded function from a metric space to a closed convex subset of a Banach space is the pointwise limit of a usco-bounded sequence of continuous functions.
Banach spaces of bounded Szlenk index
For a countable ordinal α we denote by 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 admits a separable, reflexive universal space. We also show that spaces in the class embed into spaces of the same class with a basis. As a consequence we deduce that each is analytic in the Effros-Borel structure of subspaces of C[0,1].
Banach spaces of bounded Szlenk index II
For every α < ω₁ we establish the existence of a separable Banach space whose Szlenk index is and which is universal for all separable Banach spaces whose Szlenk index does not exceed . 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.
Banach Spaces Over Topological Semifields and Common Fixed Points
Banach-Mazur game played in partially ordered sets
Concepts, definitions, notions, and some facts concerning the Banach-Mazur game are customized to a more general setting of partial orderings. It is applied in the theory of Fraïssé limits and beyond, obtaining simple proofs of universality of certain objects and classes.
Banach's Mappings And Some Generalizations
Barely Baire spaces
Base-base paracompactness and subsets of the Sorgenfrey line
A topological space is called base-base paracompact (John E. Porter) if it has an open base such that every base has a locally finite subcover . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.