Unit Code: MTH804

Unit Name: Topology

Description: This course is designed to introduce students to an important foundation of advanced mathematics. This course includes Countable and uncountable sets, Topological Spaces and Basis for a topology, The order topology, Continuous functions, Product topology, The Metric topology, The Quotient topology, Connected spaces, Components and Local connectedness, Compact spaces, Limit point compactness, Local compactness, The Countability Axioms, Separation Axioms, Normal Spaces, The Urysohn Lemma, The Tietze extension theorem, Tychonoff Theorem, The Stone-Cech Compactification, Metrization Theorems and Paracompactness, The Nagata-Smirnov Metrization Theorem.

Learning Target Outcomes: As a result of successfully completing this course, the student will be able to: 1. Generate countable and uncountable sets. 2. Demonstrate accurate and efficient use of topology techniques and capacity for mathematical reasoning through analyzing, proving and explaining concepts from topology; 3. Apply problem-solving using topology techniques applied to diverse situations in physics, engineering and other mathematical contexts; 4. Explain the proofs of the Urysohn metrinization theorem, the Tietze extension theorem and the Tychonoff Topology Theorem. 5. Explain the theorems related to Complete Metric Spaces and Function Spaces, Baire Spaces and Dimension Theory.

Prerequisite: Minimum Entry Requirements of the programme

Prerequisite Sentence: Minimum Entry Requirement of the programme

Credit Point: 30

Offered In: Semester 1,2