Function classes of Cauchy continuous maps

Description

Presenting an intriguing aspect of the theory of extensions of continuous maps, especially maps on T_1 Cauchy spaces and Hausdorff convergence spaces, this volume represents an important contribution to understanding the structural properties of these function classes. Guided by the internal description of an extension Y of a space X by means of a suitable Cauchy structure on X, it investigates both their algebraic and topological structures.Using this internal description of the extension space Y, this reference views the class of real-valued functions on X, continuously extendable to Y, as the class of real-valued Cauchy continuous maps on the related Cauchy space. By placing function classes in this natural setting, the category of Cauchy spaces, the book opens up simple solutions to various topological problems._Function Classes of Cauchy Continuous Maps_ unites the theory of extensions and function classes with the theory of Cauchy spaces, completions, and Cauchy continuous maps... compares the function classes of Cauchy continuous maps withe the well-known function classes of continuous maps... surveys the essential part of the theory of Cauchy spaces related to extensions in a logically coherent manner... explains Cauchy spaces with respect to the categories of nearness and merotopic spaces... and adds schemes to elucidate the relations between the various categories.A unique application of Cauchy spaces to the theory of function classes, _Function Classes of Cauchy Continuous Maps_ is an authoritative reference for topologists, analysts, and graduate students in these fields.