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Introduction to Topology


MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Topology eBooks . We hope mathematician or person who’s interested in mathematics like these books.


Introduction to Topology written by NA This is an other great mathematics book cover the following topics.

  • 1. Topology
    Metric Spaces, Open Sets (in a metric space), Closed Sets (in a metric space), Topological Spaces, Closed Sets (Revisited), Continuity, Homeomorphisms, Homeomorphism Examples, Theorems On Homeomorphism, Homeomorphisms Between Letters of Alphabet, Topological Invariants, Vertices, Holes, Classification of Letters, The curious case of the “Q”, Topological Invariants, Hausdorff Property, Compactness Property, Connectedness and Path Connectedness Propertie

  • 2. Making New Spaces From Old
    Cartesian Products of Spaces, The Product Topology, Properties of Product Spaces, Identification Spaces , Group Actions and Quotient Spaces

  • 3. First Topological Invariants
    Introduction, Compactness, Preliminary Ideas, The Notion of Compactness, Some Theorems on Compactness, Hausdorff Spaces, Spaces, Compactification, Motivation, One-Point Compactification, Theorems, Examples, Connectedness, Introduction, Connectedness, Path-Connectedness

  • 4. Surfaces
    Surfaces, The Projective Plane, RP2 as lines in R, 3 or a sphere with antipodal points identified, The Projective Plane as a Quotient Space of the Sphere, The Projective Plane as an identification space of a disc, Non-Orientability of the Projective Plane, Polygons, Bigons, Rectangles, Working with and simplifying polygons, Orientability, Definition, Applications To Common Surfaces, Conclusion, Euler Characteristic, Requirements, Computation, Usefulness, Use in identification polygons, Connected Sums, Definition, Well-definedness, Examples, RP, 2#T= RP, 2#RP, 2#RP, Associativity, Effect on Euler Characteristic , Classification Theorem, Equivalent definitions, Proof

  • 5. Homotopy and the Fundamental Group
    Homotopy of functions, The Fundamental Group, Free Groups, Graphic Representation of Free Group, Presentation Of A Group, The Fundamental Group, Homotopy Equivalence between Spaces, Homeomorphism vs. Homotopy Equivalence, Equivalence Relation, On the usefulness of Homotopy Equivalence, Simple-Connectedness and Contractible spaces, Retractions, Examples of Retractions, Computing the Fundamental Groups of Surfaces: The Seifert-Van Kampen Theorem, Examples, Covering Spaces, Lifting

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