Bijections of scattered spaces onto compact Hausdorff
Bi-Lipschitz Bijections of Z
It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
Bilipschitz embeddings of metric spaces into euclidean spaces.
When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small ("snowflake") deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat technical)...
Binding spaces: A unified completion and extension theory
Binormality of Banach spaces
We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space is not binormal.
Bitopological hyperspaces equipped with upper semi-finite snd lower semi-finite topologies
Bitopological local Lindelöfness
Bitopological spaces from quasi-proximities
Bochner's formula for harmonic maps from Finsler manifolds
Let ϕ :(M,F)→ (N,h) be a harmonic map from a Finsler manifold to any Riemannian manifold. We establish Bochner's formula for the energy density of ϕ and maximum principle on Finsler manifolds, from which we deduce some properties of harmonic maps ϕ.
Bodové množiny [Book]
Boolean Rings that are Baire Spaces
∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions on the corresponding...
Booleanization of uniform frames
Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.
Borel classes of uniformizations of sets with large sections
We give several refinements of known theorems on Borel uniformizations of sets with “large sections”. In particular, we show that a set B ⊂ [0,1] × [0,1] which belongs to , α ≥ 2, and which has all “vertical” sections of positive Lebesgue measure, has a uniformization which is the graph of a -measurable mapping. We get a similar result for sets with nonmeager sections. As a corollary we derive an improvement of Srivastava’s theorem on uniformizations for Borel sets with sections.
Borel sets in compact spaces: some Hurewicz type theorems
Borsuk's Theory of Shape and Cech Homotopy.
Bounded linear operators in probabilistic normed space.
Boundedness in uniform spaces and topological groups
Calibres, compacta and diagonals
For a space Z let 𝒦(Z) denote the partially ordered set of all compact subspaces of Z under set inclusion. If X is a compact space, Δ is the diagonal in X², and 𝒦(X²∖Δ) has calibre (ω₁,ω), then X is metrizable. There is a compact space X such that X²∖Δ has relative calibre (ω₁,ω) in 𝒦(X²∖Δ), but which is not metrizable. Questions of Cascales et al. (2011) concerning order constraints on 𝒦(A) for every subspace of a space X are answered.
Canonical partition relations and point character of -spaces