The closed finite-to-one mappings and their applications

In this paper,we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications.It is proved that point-G_δ properties,■-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings.By the relationships between the weak first-countabilities,we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability,quasi-first-countability,snf-countability,gfcountability and sof-countability.Furthermore,these results are applied to the study of symmetric products of topological spaces.

TRANSFER OPEN OR CLOSED SETVALUED MAPPING AND GENERALIZ－ATION OF H－KKM THEOREM WITH APPLICATIONS

In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7].

Base-mesocompact Spaces

In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained：（1） Let X be base-mesocompact and X＇ an F σ subset of X.If X is normal,then X＇ is base-mesocompact relative to X.（2） Let f：X → Y be a base-mesocompact mapping,ω（X） be a regular cardinality of X and ω（X） ≥ ω（Y）.If Y is base-mesocompact and regular,then X is base-mesocompact.（3） Let f：X → Y be a closed lindelof mapping with regular domain and regular range.If Y is base-mesocompact,then X is base-mesocompact.（4） Let X be base-mesocompact.If Y is locally compact and base-mesocompact,then X × Y is base-mesocompact.

A GENERALIZATION OF BROWDER'S FIXED POINT THEOREM WITH APPLICATIONS

The purpose of this paper is to obtain a generalization of the famous Browder's fixed point theorem and some equivalent forms. As application, these results are utilized to study the existence problems of fixed points and nearest points.

Robinson-Ursescu Theorem in p-normed Spaces

For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.

Images on Locally Separable Metric Spaces

In this paper internal characterizations on certain quotient images of locally separable metric spaces are discussed.We obtain some descriptions of quotient s-images,pseudo-open s- images,quotient compact images and closed images of locally separable metric spaces,and establish some relations between these and certain quotient images of metric spaces by the local separability of suitable subspaces.

The Change-Base Issue for Ω-Categories

Let G:Ω→Ω′be a closed unital map between commutative,unital quantales. G induces a functor G from the category of Ω-categories to that of Ω′-categories.This paper is concerned with some basic properties of G.The main results are:(1) when Ω,Ω′are integral,G:Ω→Ω′and F:Ω′→Ωare closed unital maps,F is a left adjoint of G if and only if F is a left adjoint of G;(2) G is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for G to preserve completeness in the sense that GA is a complete Ω′-category whenever A is a complete Ω-category.