David maps are generalizations of classical planar quasiconformal maps for which the dilatation is allowed to tend to infinity in a controlled fashion. In this note we examine how these maps distort Hausdorff dimension. We show: – Given α and β in [0, 2] , there exists a David map φ: C → C and a compact set Λ such that dimH Λ = α and dimH φ(Λ) = β . – There exists a David map φ: C → C such that...

Generalizing Duality Theorem of V. V. Fedorchuk [11], we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous skeletal maps, the quasi-open perfect maps, the open maps, the open perfect maps. In particular, a Stone-type duality theorem for the category of all c...

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type I operators in non-compact settings in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type I operators in non-compact settings, we shall use the concept of e...

Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as natural asymmetric generalization concept fuzzy metric sense Kramosil Michalek. Ever since, various authors have discussed several aspects such spaces, including their topological (quasi-)metric properties well connections with domain theory relationship other structures. In particular, development fixed p...

We consider a multi-criterion Boolean programming problem with partial criteria of the kind MIN MODUL of linear functions. We investigate such type of stability which can be understood as a discrete analogue of the Hausdorff lower semi-continuity. A formula of the quasi-stability radius is obtained. Mathematics Subject Classification 2000: 90C09, 90C29, 90C31.

This paper extends the theory of turbulence of Hjorth to certain classes of equivalence relations that cannot be induced by Polish actions. It applies this theory to analyze the quasi-isometry relation and finite Gromov-Hausdorff distance relation in the space of isometry classes of pointed proper metric spaces, called the Gromov space.

An approach to point-free geometry based on the notion of a quasi-metric is proposed in which the primitives are the regions and a non symmetric distance between regions. The intended models are the bounded regular closed subsets of a metric space together with the Hausdorff excess measure.

Multi-objective (vector) combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability) are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05...