We now come to two volume set on *Introduction to Topology * by *Yu. Borisovich, N. Bliznyakov, Ya. Izrailevich, T. Fomenko. *

This is a two volume book set, which has 5 sections in all. It is based on lectures delivered by Yu. G. Borisovich at Mathematics Department of Voronezh University. Each of

the section is preceeded by an illustration which has a lot of mathematical content which are by Prof. A. T. Fomenko.

About the book

This textbooks is one of the many possible variants of a first course in topology and is written in accordance with both the author’s preferences and their experience as lecturers and researchers. It deals with those areas of topology that are most closely related to fundamental courses in general mathematics and applications. The material leaves a lecturer a free choice as to how he or she may want to design his or her own topology course and seminar classes.

The books were translated from the Russian by Oleg Efimov and was

first published by Mir Publishers in 1980.

Thanks to the original uploader for the scan.

Note: The scan quality is poor and text is barely readable at

times. We have added OCR, which is not reliable, reduced file size, combined 2 pdfs into

one, bookmarked and paginated and pdfs. Vol. 1 and Vol. 2 which are

physically separate books have been combined in one single pdf. The

page numbering is continuous between the two volumes. Page 147 onwards are

the contents of Vol. 2. We have access to the hard copies, and might see a better version in the future.

PDF | Bookmarked | Paginated | OCR | Cover | 324 Pages | 24.2 MB

Update 02 Jan 2020

** Contents**

**FIRST NOTIONS OF TOPOLOGY**

1. What is topology? 11

2. Generalization of the concepts of space and function 15

3. From a metric to topological space 18

4. The notion of Riemann surface 28

5. Something about knots 34

Further Reading 37

**GENERAL TOPOLOGY**

1. T opological spaces and continuous mappings 41

2. Topology and continuous mapping of metric spaces. Spaces R^n,

S^(n-1) and D^n 46

3. Factor space and quotient topology 52

4. Classification of Surfaces 57

5 . Orbit Spaces. Projective and Iens spaces 67

6. Operations over sets in topological space 70

7. Operations over sets in metric spaces. Spheres and

balls. Completeness 73

8. Properties of continuous Mappings 76

9. Products of topological spaces 80

10. Connectedness of topological spaces 84

11. Countability and separation axioms 88

12. Normal spaces and functional separability 92

13. Compact spaces and their mappings 97

14. Compactifications of topological spaces. Metrization 105

Further Reading 107

**HOMOTOPY THEORY**

1. Mapping space. Homotopies, retractions, and deformations 111

2. Category, functor and algebraization of topological problems 118

3. Functors of homotopy grous 121

4. Computing the fundamental homotopy groups of some space 131

Further Reading 146

**MANIFOLDS AND FIBRE BUNDLES**

1. Basic notions of differential calculus in n-dimensional space 149

2. Smooth submanifolds in Euclidean space 157

3. Smooth Manifolds 161

4. Smooth functions in a manifold and smooth partition of unity 173

5. Mapping of manifolds 180

6. Tangent bundle and tangential map 188

7. Tangent vector as differential operator. Differential of function

and cotangent bundle 199

8. Vector fields on smooth manifolds 208

9. Fibre bundles and covering 213

10. Smooth function on manifold and cellular structure of manifold (example) 235

11. Non-degenrate ciritcal point and its index 240

12. Describing homotopy type of manifold by means of critical values 244

Further Reading 249

**HOMOLOGY THEORY**

1. Preliminary Notes 253

2. Homology groups of chain complexes 255

3. Homology groups of simplical complexes 257

4. Singular Homology Theory 268

5. Homology theory axioms 278

6. Homology groups of spheres. Degree of mapping 281

7. Homology groups of cell complexes 289

8. Euler Characteristic and Lefschetz number 292

Further reading 299

Illustrations 302

References 303

Name Index 306

Subject Index 308

wov this is great, thanks

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This is a dead link. I downloaded the zip file so I could continue reading the book I had purchased but that I can’t find right now. It was 23 MB. When I went to extract it, an error saying no extract location came. I am not sure if this is a virus.

Your better bet is to get this book from a library. It is there in yeshiva university and columbia university. It takes less than an hour to scan it with their machines. Then you can use it for your own purposes.

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This link is not working. Please upload into another link.

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This link is not working. please update another location.

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Internet Archive link has been added, dead links removed. Please check.

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Kindly give another link. This link is not functional. Same link does not work for other books as well…Kindly help us….

Best

Parag

India

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Internet Archive link has been added, dead links removed. Please check.

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the link is dead or nonfunctional

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Internet Archive link has been added, dead links removed. Please check.

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the link doesn’t work…..

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Internet Archive link has been added, dead links removed. Please check.

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Thank you!!!! I must say that this is a great website!!! Hats off and loads of thanks!!!

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Thanks!

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