集值映射族的紧性

Compactness of Set-Valued Mapping Family

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 different.