【摘要】 <正> 映射族的紧性在分析学中的重要性是众所周知的.如在微分方程、积分方程、变分法、保形映射等理论中都曾用到.几十年来许多人将它推广为各种一般形式.由于映射族的种类不同,映射空间的拓扑结构不同而形式各异.本文主要就集值映射族在紧开拓扑下讨论一种特殊形式.更多还原

【Abstract】 The classical theorem of Ascoli asserts that a uniformly bounded, equicontinuous family of functions has a compact closure in the space of con tinuous functions with the topologyof uniform convergence.The theorem is very important in analytic theory, for example it is ever used in the theories of differential equation, integral equation, calculus of variations, conformal mapping. Many people have extended it to some kinds of general form in the several decades. Because of the difference of mapping family and the difference of topological structure of mapping sace, the form is dif-ferent .The purpose of this paper is to improve the Gale-type multifunction Ascoli theorem of Mancuso [1] . The main results of this paper are.Theorem Let be a family of point-compact continuous multifunctions on a K-space X to a T1 regular Y, is compact iff satisfies condi-tions .a . is closed in point-compact multifunctions for compact open topo-logyb. [x] is compact for all x∈X.c. for each closed subset of ,the ∩{F+(G) . F∈ } and ∩{F(G):F∈. } are open in X whenever G is open in Y.更多还原