In 1975, M. M. Choban [5] introduced a new topology on the set of all closed subsets of a topological space, similar to the but weaker than it. In 1998, G. Dimov and D. Vakarelov [8] used a generalized version of this new topology, calling it . The present paper is devoted to a detailed study of...

In the paper we investigate Borel classes of multivalued functions of two variables. In particular we generalize a result of Marczewski and Ryll-Nardzewski [6] concerning of real function whose ones of its sections are right-continuous and other ones are of Borel class , into the case of...

The Morita equivalence of m-regular involutive quantales in the context of the theory of Hilbert A-modules is presented. The corresponding fundamental representation theorems are shown. We also prove that two commutative m-regular involutive quantales are Morita equivalent if and only if they...

Given a cover of a quasi-uniform space we introduce a concept of lower semicontinuity for multifunctions : → 2 , called -lsc. In this way, we get a common description of Vietoris-lsc, Hausdorff-lsc, and bounded-Hausdorff-lsc as well. Further, we examine set-theoretical and vector operations on...

Every topological group has some natural compactifications which can be a useful tool of studying . We discuss the following constructions: (1) the () is the compactification corresponding to the algebra of all right uniformly continuous bounded functions on ; (2) the () corresponds to the...

We give a new class of convergence criteria for the classical Newton method for the equation () = 0. We prove the global convergence, if the function is the gradient of a convex function, while the convergence in the general case is still open. Our convergence condition consists of only one...

We prove theorems of the following form: if ⊆ ℝ is a “big set”, then there exists a “big set” ⊆ ℝ and a perfect set ⊆ ℝ such that × ⊆ . We discuss cases where “big set” means: set of positive Lebesgue measure, set of full Lebesgue measure, Baire measurable set of...