Continuous Selection and Fixed Point Theorems for Fuzzy Mappings in General Topological Spaces

Continuous selection theorem is a very versatile tool in nonlinear problems arising in mathematics and applied science. Since a famous continuous selection theorem was proved by Michael (1956), many scholars have established continuous selection theorems under the setting of topological vector spaces or abstract convex spaces and have given applications in many different fields simultaneously. Inspired by the works mentioned above, this paper establishes some continuous selection theorems for fuzzy mappings in general topological spaces without any linear and convex structure on the basis of the unity partition technique, and next, as their applications, some new fixed point theorems for fuzzy mappings are obtained in general topological spaces without any linear and convex structure. Our results include the corresponding results in the recently existing literatures as special cases.