MA3L305
Undergraduate (ITEP)
· Generally offered: Autumn
Topology
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: Set theory and logic, Fundamental concepts, Functions and relations, Cartesian products, Countable and uncountable sets, Definitions and examples of topological spaces, Open sets, Basis for a topology.
Unit II: Order topology, Product topology on X×Y, Subspace topology, Closed sets and limit points, Continuous functions, Homeomorphisms.
Unit III: Metric topology, Examples and properties of metric spaces, Hausdorff spaces, Uniform limit theorem, Quotient map, Definition and examples of quotient topology.
Unit IV: Definition and examples of connected spaces, Intermediate value theorem, Path connectedness, Compact spaces, Tube lemma, Heine-Borel theorem, Extreme value theorem, Uniform continuity theorem.
Full syllabus document →
Unit II: Order topology, Product topology on X×Y, Subspace topology, Closed sets and limit points, Continuous functions, Homeomorphisms.
Unit III: Metric topology, Examples and properties of metric spaces, Hausdorff spaces, Uniform limit theorem, Quotient map, Definition and examples of quotient topology.
Unit IV: Definition and examples of connected spaces, Intermediate value theorem, Path connectedness, Compact spaces, Tube lemma, Heine-Borel theorem, Extreme value theorem, Uniform continuity theorem.
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