Elementary Point-Set Topology

Preface List of Figures List of Symbols1 Mathematical Proofs and Sets
1.1 Introduction to Elementary Logic .1.2 More Elementary Logic 1.3 Quantifiers1.4 Methods ofMathematical Proof1.5 Introduction to Elementary Set Theory 1.6 Cardinality 1.7 Cardinal Arithmetic2 Topological Spaces
2.1 Introduction 2.2 Topologies2.3 Bases2.4 Subspaces 2.5 Interior, Closure, and Boundary2.6 Hausdorff spaces2.7 Metric Spaces 2.8 Euclidean Spaces3 Continuous Functions
3.1 Review of the Function Concept3.2 More on Image and Inverse Image3.3 Continuous Functions3.4 More on Continuous Functions3.5 More on Homeomorphism 4 Product Spaces
4.1 Products of Sets4.2 Product Spaces4.3 More on Product Spaces 5 Connectedness
5.1 Introduction to Connectedness5.2 Products of Connected Spaces5.3 Connected Subsets of the Real Line 6 Compactness
6.1 Introduction to Compactness 6.2 Compactness in the Space of Real Numbers6.3 The Product of Compact Spaces 6.4 Compactness in Metric Spaces6.5 More on Compactness in Metric Spaces 6.6 The Cantor Set7 Fixed Point Theorems and Applications
7.1 Sperner's 7.2 Brouwer's Fixed Point Theorem.7.3 The Fundametnal Theorem of Algebra 7.4 Function Spaces7.5 ContractionsIndex