Borel sets in compact spaces: some Hurewicz type theorems
Borel sets of exact class
Borel sets with -section
Borel sets with σ-compact sections for nonseparable spaces
We prove that every (extended) Borel subset E of X × Y, where X is complete metric and Y is Polish, can be covered by countably many extended Borel sets with compact sections if the sections , x ∈ X, are σ-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond’s result which does not use transfinite induction.
Borel Structures and a Topological Zero-One Law.
Boréliens à coupes
Borsuk-Ulam Sätze und Abbildungen mit kompakten Iterierten [Book]
Borsuk-Ulam type theorems
A generalization of the theorem of Bajmóczy and Bárány which in turn is a common generalization of Borsuk's and Radon's theorem is presented. A related conjecture is formulated.
Boundaries of and Selectors for Upper Semi-Continuous Multi-Valued Maps.
Bounded analytic sets in Banach spaces
Conditions are given which enable or disable a complex space to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of .
Boundedness in uniform spaces and topological groups
Brouwer Fixed Point Theorem for Simplexes
In this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of εn. First we introduce the Lebesgue number, which for an arbitrary open cover of a compact metric space M is a positive real number so that any ball of about such radius must be completely contained in a member of the cover. Then we introduce the notion of a bounded simplicial complex and the diameter of a bounded simplicial complex. We also prove...
Brouwer Fixed Point Theorem in the General Case
In this article we prove the Brouwer fixed point theorem for an arbitrary convex compact subset of εn with a non empty interior. This article is based on [15].
Browder-Fan fixed point theorem and related results
Browder's fixed point theorem and some interesting results in intuitionistic fuzzy normed spaces.
Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces.
-minimal subsets of the circle
Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.
weakly chaotic functions with zero topological entropy and non- flat critical points.
-commuting maps and invariant approximations.
Can we assign the Borel hulls in a monotone way?
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....