Uniform Spaces - Brossura

Isbell, John

Brossura

ISBN 10: 0821815121 ISBN 13: 9780821815120

Casa editrice: Amer Mathematical Society, 1964

Riassunto

Uniform spaces play the same role for uniform continuity as topological spaces for continuity. The theory was created in 1936 by A. Weil, whose original axiomatization was soon followed by those of Bourbaki and Tukey; in this book use is made chiefly of Tukey's system, based on uniform coverings. The organization of the book as a whole depends on the Eilenberg-MacLane notions of category, functor and naturality, in the spirit of Klein's Erlanger Program but with greater reach.The preface gives a concise history of the subject since 1936 and a foreword outlines the category theory of Eilenberg and MacLane. The chapters cover fundamental concepts and constructions; function spaces; mappings into polyhedra; dimension 1 and 2; compactifications and locally fine spaces. Most of the chapters are followed by exercises, occasional unsolved problems, and a major unsolved problem; the famous outstanding problem of characterizing the Euclidean plane is discussed in an appendix. There is a good index and a copious bibliography intended not to itemize sources but to guide further reading.

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1964
• Lingua: Inglese
• ISBN 10: 0821815121
• ISBN 13: 9780821815120
• Rilegatura: Copertina flessibile
• Numero di pagine: 175
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile