An introduction to Point-Set-Topology Part-I

Por: Swayam . en: ,

Week 1 :Chapter I - Introduction -Introduction,Normed linear spaces (NLS),Metric Spaces,ε - Definition of continuity,Examples of continuous functions,Topological Spaces.
Week 2 :Chapter I - Introduction -Examples,Functions,Topology of the n-dim. Euclidean space,Equivalences on metric spaces,Equivalences continued.
Week 3 :Chapter I - Introduction -Counter examples,Definitions and examples,Closed sets,Interiors and boundaries,Interiors and derived sets.
Week 4 :Chapter I - Introduction -More examples, Metric Trinity, Baire’s Category Theorem, An Application in Analysis, Completion of Metric space.
Week 5 :Chapter II - Creating New Spaces -Bases and subbases,Subbases,Box Topology,Subspaces,Union of spaces.
Week 6 :Chapter II - Creating New Spaces -Extending neighbourhoods, Quotient Spaces, Product of spaces, Study of Products - continued, Induced and co-induced topologies.
Week 7 :Chapter III- Smallness Properties of Topological Spaces -Path Connectivity, Connectivity, Connected components, Connectedness-continued, Local Connectivitym, More Examples.
Week 8 :Chapter III- Smallness Properties of Topological Spaces -Compactness and Lindelöfness, Compact Metric Spaces, Compactness-continued, Countability and Separability, Types of Topological Properties.
Week 9 :Chapter III- Smallness Properties of Topological Spaces -Productive Properties, Productive Properties-continued, Tychonoff Theorem, Proof Alexander’s Subbase Theorem.
Week 10 :Chapter IV - Largeness properties -Fréchet Spaces, Hausdorff spaces, Examples and Applications, Examples and Applications - continued.
Week 11 :Chapter IV - Largeness properties -Regularity and Normality, Characterization of Normality, Tietze’s Characterization of Normal Spaces, Productiveness of Separation Axioms, The Hierarchy.
Week 12 :Chapter V - Topological groups and Topological Vector Spaces -Topological Groups, Topological Groups-continued,Topological Groups-continued,Topological Vector Spaces,Topological Vector Spaces-continued,Topological Vector Spaces-continued.