Gâteaux Differentiability of Convex Functions and Topology

This volume puts together results touching weak Asplund spaces which are currently spread throughout the literature. All subclasses are discussed, including interferences and counterexamples, with a special emphasis on topological implications.

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This text puts together "folklore results" touching weak Asplund spaces. It presents a thorough examination of weak Asplund cases. Nonseparable Banach spaces, renorming, and differentiability are stressed throughout the text and all subclasses, including inferences and counterexamples are discussed. It also covers Stegall's classes, fragmentability, and "long sequences" of linear projections. Notes, remarks and questions end each chapter.