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Description of  Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity (Dover Books on Mathematics)

Set topology, the subject of the present volume, studies sets in topological spaces and topological vector spaces whenever these sets are collections of n-tuples or classes of functions, the book recovers well-known results of classical analysis. In order to provide a topological tool of equal interest to students of both pure and applied mathematics, this work includes a systematic development of the properties of multi-valued functions. Topics include families of sets, mappings of one set into another, ordered sets, topological spaces, topological properties of metric spaces, mappings from one topological space into another, mappings of one vector space into another, convex sets and convex functions in the space R" and topological vector spaces. To render the expositions more concrete, examples have been included from very different domains. 1963 edition. Read more