000			03277nam a22003137a 4500
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020			_a9789819706037
040			_aNISER LIBRARY _cNISER LIBRARY
041			_aEnglish
082			_a515.1 _bPAR-T
100			_aParthasarathy, K. _q[Krishnan Parthasarathy]
245			_aTopology: _ban invitation
260			_aSingapore: _bSpringer, _c2022.
300			_axvii, 267p.
490			_aUNITEXT _v134 _x2038-5714
505			_a1. Apéritif: The Intermediate Value Theorem 2. Metric Spaces 3. Topological Spaces 4. Continuous Maps 5. Compact Spaces 6. Topologies Defined by Maps 7. Products of Compact Spaces 8. Separation Axioms 9. Connected Spaces 10. Countability Axioms 11. Locally Compact Spaces 12. Complete Metric Spaces 13. Combinatorial Methods in Euclidean Topology 14. Homotopy 15. Fundamental Groups and Covering Spaces
520			_aThis book starts with a discussion of the classical intermediate value theorem and some of its uncommon “topological” consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the author’s perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided. All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré–Miranda, Brouwer’s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk’s antipodal theorem, the Borsuk–Ulam theorem and the Lusternik–Schnirelmann–Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces. Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
600			_aK. Parthasarathy
650			_aTopology
650			_aPoincare theorem
650			_aFixed point
650			_aAntipodal Map
650			_aFundamental Group
650			_aDomain and Dimension Invariance
856			_uhttps://link.springer.com/book/10.1007/978-981-16-9484-4 _yTopology: An Invitation
942			_cN _2udc
999			_c34708 _d34708