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Topology General & Algebraic (2009) (Malestrom)

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D. Chatterjee , "Topology General & Algebraic"
New Age International | 2009 | ISBN: 8122419437 | 176 pages | PDF

This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the realm of differentiable manifold and fibre bundles. It should be usefull for mathematicians as well as Physicists desiring to acquire overall knowledge of algebraic topology and its tools.

Contents:

PART I
Sets, Relations and Functions
Topology of R and R2
Metric Space
Topological Spaces
Separation Axioms
Compactness
Connectedness

PART II
Algebraic Preliminaries
Homotopy Theory
Compact Open Topology
Higher Homotopy Groups
Surfaces, Manifolds and CW-complexes
Simplicial Homology Theory
Singular Homology Theory
Manifold Analysis
Fibre Bundles

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