Introduction

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By Yuri G. Borisovich, Nikolai M. Bliznyakov, Tatyana N. Fomenko, Yakov A. Izrailevich (auth.)

Topology as a topic, in our opinion, performs a critical position in collage schooling. it's not quite attainable to layout classes in differential geometry, mathematical research, differential equations, mechanics, useful research that correspond to the transitority country of those disciplines with no related to topological ideas. for this reason, it really is necessary to acquaint scholars with topo­ logical examine equipment already within the first college classes. This textbook is one attainable model of an introductory direction in topo­ logy and components of differential geometry, and it totally displays either the authors' own personal tastes and event as academics and researchers. It offers with these components of topology and geometry which are such a lot heavily relating to primary classes mostly arithmetic. the academic fabric leaves a lecturer a unfastened selection in designing his personal direction or his personal seminar. We draw recognition to a couple of particularities in our publication. the 1st chap­ ter, based on the authors' purpose, should still acquaint readers with topolo­ gical difficulties and ideas which come up from difficulties in geometry, research, and physics. the following, common topology (Ch. 2) is gifted through introducing con­ structions, for instance, with regards to the idea that of quotient areas, a lot in advance of a variety of different notions of basic topology hence making it attainable for college kids to review vital examples of manifolds (two-dimensional surfaces, projective areas, orbit areas, etc.) as topological areas, immediately.

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