MSM1201 - Advanced Topology

HNGU M.SC. MATHEMATICS SEMESTER - II 

MSM1201 – ADVANCED TOPOLOGY

Unit 1: 

• Countability Axioms: First countable space, 
• Second countable space, 
• Separable space,
• Lindeloff space

Unit 2: 

• Separation axioms- Hausdorff space, 
• Regular space, normal space, 
• Urysohn’s lemma,
• Completely regular space,
• Tietze extension theorem.

Unit 3: 

• Imbedding of Manifolds, 
• Partition of unity, 
• Tychonoff theorem (statement only), 
• TheStone-cech Compactifications and uniqueness.

Unit 4: 

• Complete metric space,
• Compactness in metric spaces,
• Ascoli’s theorem, Bair spaces,
• Baire category theorem.

Download Reference Books:

The course is covered by Topology – J. R. Munkres, Prentice – Hall of India, 1992.

1. General Topology – S. Willard, Addison Wesley, 1970.

2. Topology – J. Dugundji, Prentice – Hall of India, 1975.

3. Aspects of Topology – C. O. Christonson and W. l. Voxman, Marcel Dekker Inc, 1977.

4. General Topology – J. L. Kelley, D. Van Nostraml, 1950.

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