Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: (1) Some of the classes which were different for open covers are equal for Borel covers – Section 1; (2) Some Borel classes coincide with classes that have been studi...

We consider countable Borel equivalence relations on quotient Borel spaces. We prove a generalization of the representation theorem of Feldman–Moore, but provide some examples showing that other very simple properties of countable equivalence relations on standard Borel spaces may fail in the context of nonsmooth quotients. In this paper we try to analyze some very basic questions about the str...

The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field theory. We observe that the rate of convergence can be improved by the application of Padé approximants to the Borel transform expressed as a function of the co...

The article investigates the sceptical challenge from an information-theoretic perspective. Its main goal is to articulate and defend the view that either informational scepticism is radical, but then it is epistemologically innocuous because redundant; or it is moderate, but then epistemologically beneficial because useful. In order to pursue this cooptation strategy, the article is divided in...

The optimal conformal mapping of the Borel plane was recently used to accelerate the convergence of the perturbation expansions in QCD. In this work we discuss the relevance of the method for the calculation of the Laplace-Borel integral expressing formally the QCD Green functions. We define an optimal expansion of the Laplace-Borel integral in the principal value prescription and establish con...

Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F ) is a Borel subset of M if F is closed in L. We show that then f−1(y) is a Kσ set for all except countably many y ∈M , that M is also Luzin, and that the Borel classes of the sets f(F ), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the cla...

We prove that the topological statement: “Any compact covering mapping between two Borel sets is inductively perfect” is equivalent to the set-theoretical statement: “ ∀α ∈ ωω , א 1 < א1”. The starting point of this work is the following topological problem: Problem. Is any compact covering mapping between two Borel spaces inductively perfect? We recall that if f : X → Y is a continuous and ont...