The authors apply their recent work on the Lyapunov theorem in locally convex Hausdorff spaces to the bang-bang principle for control systems in infinite dimensions. They show that the bang-bang principle holds for every integrably bounded, measurable, weakly compact convex-valued multifunction if and only if the underlying measure space is saturated. They also demonstrate the equivalence of th...

This paper reviews the one-to-one correspondence between stably compact spaces (a topological concept covering most classes of semantic domains) and compact ordered Hausdorff spaces. The correspondence is extended to certain classes of real-valued functions on these spaces. This is the basis for transferring methods and results from functional analysis to the non-Hausdorff setting. As an applic...

in this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of a.p. sostak's and ramadan is introduced. some interesting properties and characterizations of them are investigated. also, some applications to fuzzy compact spaces are established.

Let us consider two compact connected and locally connected Hausdorff spaces M , N and two continuous functions φ : M → R, ψ : N → R . In this paper we introduce new pseudodistances between pairs (M,φ) and (N,ψ) associated with reparametrization invariant seminorms. We study the pseudodistance associated with the seminorm ‖φ‖ = maxφ − minφ, denoted by δΛ, and we find a sharp lower bound for it....

In this paper, we give important properties as completeness, completion and precompactness of Hausdorff intuitionistic fuzzy metric spaces which is given by Gregori et al [13] and establish the precise relationship between the Hausdorff metric of a metric space (X, d) and the Hausdorff intuitionistic fuzzy metric of the standart intuitionistic fuzzy metric of d, and give two examples. AMS Subje...

In this paper, we construct a class of Hausdorff spaces with the property that nonempty compact subsets of these spaces that have the same cardinality are homeomorphic Theorem 3.7 . Conditions are given for these spaces to be compact Corollary 2.10 . Also, it is shown that these spaces contain compact subsets that are infinite Corollary 2.10 . This paper uses the Zermelo-Fraenkel axioms of set ...

In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.

This paper is one in a series that investigates topological measures on locally compact spaces. A measure defined open and closed sets; it finitely additive the collection of sets, inner regular outer sets. We examine semisolid sets give way constructing from solid-set functions compact, Hausdorff, connected, connected For spaces we present two simpler methods than currently available one. exam...

for K a compact subset of A and W an open subset of B [2]1. Now let X and Y be Hausdorff spaces, and let Z be an arbitrary topological space. Let XX Y be the topological product of X and Y. We shall be concerned with the compact-open topologized spaces Zxxr, Zx, and (ZX)Y. R. H. Fox [2] has related these spaces, taking Zx as compact-open topologized, but not considering topologies on the more c...