Topology Without Tears

Description

"Including a graduate course on Topological Groups" - Version 2024-08-06 Downloaded from https://topologywithouttears.net/ - Author homepage at https://sidneymorris.net Introduction Acknowledgments Readers – Locations and Professions Readers' Compliments Helpful Hint on Hyperlinks The Author Credits for Images Topological Spaces Topology Open Sets Finite-Closed Topology Postscript The Euclidean Topology Euclidean Topology Basis for a Topology Basis for a Given Topology Postscript Limit Points Limit Points and Closure Neighbourhoods Connectedness Postscript Homeomorphisms Subspaces Homeomorphisms Non-Homeomorphic Spaces Postscript Continuous Mappings Continuous Mappings Intermediate Value Theorem Postscript Metric Spaces Metric Spaces Convergence of Sequences Completeness Contraction Mappings Baire Spaces Postscript Compactness Compact Spaces The Heine-Borel Theorem Postscript Finite Products The Product Topology Projections onto Factors of a Product Tychonoff's Theorem for Finite Products Products and Connectedness Fundamental Theorem of Algebra Postscript Countable Products The Cantor Set The Product Topology The Cantor Space and the Hilbert Cube Urysohn's Theorem Peano's Theorem Postscript Credits for Images Tychonoff's Theorem The Product Topology For All Products Zorn's Lemma Tychonoff's Theorem Stone-C̆ech Compactification Postscript Credit for Images Quotient Spaces Quotient Spaces Identification Spaces Möbius Strip, Klein Bottle and Real Projective Space Postscript Credit for Images The Stone-Weierstrass Theorem The Weierstrass Approximation Theorem The Stone-Weierstrass Theorem Credit for Images Appendix 1: Infinite Sets Appendix 2: Topology Personalities Appendix 3: Chaos Theory and Dynamical Systems Appendix 4: Hausdorff Dimension Appendix 5: Topological Groups: A Graduate Course Appendix 6: Filters and Nets Bibliography Index