We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of “simple” retractions. Consequently, a compact space of weight 6 א1 is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight 6 א1 is preserved both under ret...

The objective of this paper is to obtain the properties of αψcompact spaces by using nets, filterbase, αψ-complete accumulation points and so on. We also investigate some properties of αψ-continuous multifunctions and αψ-compact spaces in the context of multifunction.

We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other chara...

The purpose of this article is to develop the basic theory of stably compact spaces (=compact, locally compact, coherent sober spaces) and introduce in an accessible manner with a minimum of prerequisites significant new lines of their investigation and application arising from recent research, primarily in the theoretical computer science community. There are three primary themes that are deve...

A family of compact spaces containing continuous images of Radon-Nikodým compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikodým compact K we prove: If K is totally disconnected, then it is Radon-Nikodým compact. If K is adequate, then it is even Eberl...

The aim of this paper is the construction of pseudo-Riemannian homogeneous spaces with special curvature properties such as Einstein spaces etc. using corresponding known compact Riemannian ones. This construction is based on the notion of a certain duality between compact and non-compact homogeneous spaces.

The problem, whether every topological space has a weak compact reflection, was answered by M. Hušek in the negative. Assuming normality, M. Hušek fully characterized the spaces having a weak reflection in compact spaces as the spaces with the finite Wallman remainder. In this paper we prove that the assumption of normality may be omitted. On the other hand, we show that some covering propertie...

It will be convenient to call a space X a ParoviZenko space if (cy) X is a zero-dimensional compact space without isolated points, (p) every two disjoint open F,-sets have disjoint closures, and (y) every nonempty GG-set in X has non-empty interior. Compact spaces satisfying (p) are usually called F-spaces, while spaces satisfying (y) are called almost-P spaces. Examples of F-spaces are the ext...

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local

Method of the solution of the main problem of homogeneous spaces thermodynamics on non-compact spaces in the case of non-compact homogeneous spaces is presented in the article. The method is based on the formalism of coadjoint orbits. In that article we present algorithm that allows e ciently evaluate heat kernel on non-compact homogeneous spaces. The method is illustrated with non-trivial exam...