By Paul Alexandroff
Alexandroff's attractive and chic creation to topology used to be initially released in 1932 as an extension of yes features of Hilbert's Anschauliche Geometrie. The textual content has lengthy been well-known as one of many best displays of the elemental techniques, important for mathematicians who haven't time for broad learn and for starting investigators.
The ebook isn't really an alternative to a scientific textual content, yet an surprisingly necessary intuitive method of the fundamental suggestions. Its target is to give those ideas in a transparent, trouble-free type with no sacrificing their profundity or exactness and to provide a few indication of the way they're helpful in more and more parts of arithmetic. the writer proceeds from the fundamentals of set-theoretic topology, via these topological theorems and questions that are dependent upon the idea that of the algebraic advanced, to the idea that of Betti teams which binds jointly valuable topological theories in a complete and upon which purposes of topology principally rest.
Wholly in line with present investigations, within which a bigger and bigger a part of topology is ruled by way of the idea that of homology, the e-book bargains essentially with the innovations of advanced, cycle, and homology. It issues the best way towards a scientific and completely geometrically orientated conception of the main basic constructions of space.
First English translation, ready for Dover through Alan E. Farley. Preface via David Hilbert. Author's Foreword. Index. 25 figures.
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II. Algebraic Complexes . . . . . III. Simplicial Mappings and Invariance Theorems . . . . . . . . Index . . . . . . . . .
Polyhedra, Manifolds, Topological areas . II. Algebraic Complexes . . . . . III. Simplicial Mappings and Invariance Theorems . . . . . . . . Index . . . . . . . . .
III. Simplicial Mappings and Invariance Theorems . . . . . . . . Index . . . . . . . . .