By Paul Alexandroff
Alexandroff's appealing and chic creation to topology was once initially released in 1932 as an extension of convinced points of Hilbert's Anschauliche Geometrie. The textual content has lengthy been famous as one of many best shows of the elemental innovations, very important for mathematicians who haven't time for broad learn and for starting investigators.
The publication isn't really an alternative choice to a scientific textual content, yet an strangely important intuitive method of the fundamental thoughts. Its goal is to provide those strategies in a transparent, ordinary style with out sacrificing their profundity or exactness and to offer a few indication of ways they're worthwhile in a growing number of parts of arithmetic. the writer proceeds from the fundamentals of set-theoretic topology, via these topological theorems and questions that are established upon the concept that of the algebraic complicated, to the idea that of Betti teams which binds jointly significant topological theories in a complete and upon which functions of topology principally rest.
Wholly in step with present investigations, within which a bigger and bigger a part of topology is ruled via the concept that of homology, the booklet offers essentially with the ideas of advanced, cycle, and homology. It issues the best way towards a scientific and completely geometrically orientated thought of the main basic constructions of space.
First English translation, ready for Dover by means of Alan E. Farley. Preface by way of David Hilbert. Author's Foreword. Index. 25 figures.