In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4].
Ji-cheng HouDepartment of Mathematics, Shantou University, Shantou 515063, ChinaCorrespondence address: Department of Mathematics and Information Science, Yantai University, Yantai264005, China
For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.
Some properties of semi-continuous functions are investigated, and some characterizations of semi-stratifiable spaces with semi-continuous functions are given.
In pattern analysis and image management, the information of an objective image can be recovered from a sequence approximate images. In mathematical form of expression it is needed to consider some types of continuity. Many researchers defined the limit and the upper limit of a sequence and, using the concepts, characterized continuity in the space consisted of images. In the present paper, the authors give firstly some examples to show that there axe some theoretical shortcomings in those results, then give some corresponding correct results.
