Algebraic Topology
De Gruyter (Verlag)
978-3-11-151736-0 (ISBN)
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The book contains a large number of examples and exercises. One chapter is fully devoted to the construction of the fundamental groups of some surfaces and topological spaces. Borsuk's theory of retracts is fully developed in one chapter, too. Five sections of this chapter address the different facets of the important theory connected with homotopy, homology, and topological degree theories. This chapter sections, together with the homotopy theory developed earlier, can serve as additional course material for students involved in General Topology. In addition, the book presents some results on the solvability of some nonlinear differential equations subject to initial or boundary conditions. The book does not report long and heavy technical proofs of some advanced theorems which can be found in most specialized textbooks. The book comprises 270 detailed examples, 310 exercises (with hints), 70 illustrative figures, and 70 commutative diagrams to make it more oriented towards applications.The textbook is practical both as a teaching and research document for Bachelor, Master students, and first-year PhD students, as well. It is also suitable for advanced undergraduate students and independent researchers.
Dr S. Djebali received a Master degree (1983) and a PhD degree (1987) in Mathematics from Paris XI University (France,) then a Science Doctorate (Habilitation) from Algiers University (2001).
S. Djebali is specialized in Mathematical Analysis with a major in Fixed point Theory and Applications to Differential Equations (Index fixed point and topological degree, Topological structure of solution set for differential equations and inclusions). Yet, the author has skills in Nonlinear Analysis (Variational and Topological methods), Applied Analysis (mainly in Integro-Differential Equations and Inclusions), and Algebraic Topology.
Web localization and visibility:
Research gate: https://www.researchgate.net/profile/Smail_Djebali/
https://members.imamu.edu.sa/staff/ibdjebali/en/Pages/default.aspx
MathSciNet ID: 643955
Zentrablatt: djebali.smail
dblp: 02/5426
Orcid ID: http://orcid.org/0000-0002-2318-1989
Publons ID: 1751998 (WoS: A-1503-2012)
Scopus Author ID: 14064587500
Google Scholar Profile (H-index=16 - i10-index=36 - 1045 citations):
http:scholar.google.com/citations?user=mwyKeMsAAAAJ&hl=en&oi=sra
Previous books by Authors (including year, title, publisher):
- Existence and Structure of Solution Sets for Impulsive Differential Inclusions: a Survey" (joint work with L. Gorniewicz and A. Ouahab), Lecture Notes of the Schauder Center for Nonlinear Studies (Torun, Poland), Vol. 13, Feb. 2012 (pp. 148)
- Solution Sets for Differential Equations and Inclusions", (joint book with L. Gorniewicz and A. Ouahab), "De Gruyter Series in Nonlinear Analysis and Applications, 18", Walter De Gruyter, Berlin, Germany, 2012, xix+453 pp. appeared 14 November 2012) ISBN: 978-3-11-029356-2. DOI: 0.1515/9783110293562. http://www.degruyter.com/view/product/184567.
- Fixed Point Theorems with Applications. (joint book with Karima Mebarki, Svetlin G. Georgiev, and Khaled Zennir). Copyright Year 2023. ISBN 9781032464961. May 12, 2023 Forthcoming by Chapman & Hall. 430 Pages
| Erscheint lt. Verlag | 16.12.2024 |
|---|---|
| Reihe/Serie | De Gruyter Textbook |
| Zusatzinfo | 70 b/w and 5 col. ill., 2 b/w and 0 col. tbl. |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Adjunction Spaces and Similar Constructions • Basic Constructions in General Topology • Fixed point theorems • Homeomorphism and Homotopy Equivalences • Homotopy and Homology Groups |
| ISBN-10 | 3-11-151736-5 / 3111517365 |
| ISBN-13 | 978-3-11-151736-0 / 9783111517360 |
| Zustand | Neuware |
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