On quasicontinuous and cliquish functions
On quasi-continuous bijections.
On quasi-continuous functions having Darboux property.
On quasidomination of compacta
On quasi-p-bounded subsets
The notion of quasi-p-boundedness for p ∈ is introduced and investigated. We characterize quasi-p-pseudocompact subsets of β(ω) containing ω, and we show that the concepts of RK-compatible ultrafilter and P-point in can be defined in terms of quasi-p-pseudocompactness. For p ∈ , we prove that a subset B of a space X is quasi-p-bounded in X if and only if B × is bounded in X × , if and only if , where is the set of Rudin-Keisler predecessors of p.
On quasi-uniform convergence of a sequence of s.q.c. functions
On quasi-uniform space valued semi-continuous functions
F. van Gool [Comment. Math. Univ. Carolin. 33 (1992), 505–523] has introduced the concept of lower semicontinuity for functions with values in a quasi-uniform space . This note provides a purely topological view at the basic ideas of van Gool. The lower semicontinuity of van Gool appears to be just the continuity with respect to the topology generated by the quasi-uniformity , so that many of his preparatory results become consequences of standard topological facts. In particular, when the order...
On recurrent functions.
On reflexive closed set lattices
For a topological space , let denote the set of all closed subsets in , and let denote the set of all continuous maps . A family is called reflexive if there exists such that for every . Every reflexive family of closed sets in space forms a sub complete lattice of the lattice of all closed sets in . In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families of closed...
On regular Stein neighborhoods of a union of two totally real planes in ℂ²
We find regular Stein neighborhoods of a union of totally real planes M = (A+iI)ℝ² and N = ℝ² in ℂ², provided that the entries of a real 2 × 2 matrix A are sufficiently small. A key step in our proof is a local construction of a suitable function ρ near the origin. The sublevel sets of ρ are strongly Levi pseudoconvex and admit strong deformation retraction to M ∪ N.
On relations approximated by continuous functions
On rest points of dynamical systems
On restrictive semigroups of continuous functions
On rings of Darboux functions
On -cluster sets and -closed spaces.
On -metrizable spaces
On Scheepers' conjecture
On selections of multifunctions
The purpose of this paper is to introduce a definition of cliquishness for multifunctions and to study the search for cliquish, quasi-continuous and Baire measurable selections of compact valued multifunctions. A correction as well as a generalization of the results of [5] are given.
On semi -perfect functions.
On semi-closed sets and semi-open sets and their applications