This article introduces three kinds of equal value definitions of function continuity, proves the equal value relation among them, and makes people understand further the continuity of function.

In this paper we introduce the concept of continuity of a fuzzy sample function, and solve the basic theoretical problem of continuity of fuzzy stochastic processes successfully.

Cantor, the paper presents conditions of uniform continuity of a function in arbitrary boundary, and discusses the simple distinguish method for nonuniform continuity.