MSM1102 - General Topology

HNGU M.SC. MATHEMATICS SEMESTER - I

MSM1102 - GENERAL TOPOLOGY

Unit 1: 

• Topological Spaces,
• Basis and sub-basis for a topology, The order topology, 
• The product space 𝛱 Xi (for finitely many topological spaces only), 
• Subspace topology,
• Closed sets, limit points.

Unit 2: 

• Continuous Functions,
• Homeomorphisms, 
• The pasting lemma,
• Map into products, 
• The metric topology, 
• The sequence lemma, 
• Uniform limit theorem,
• The quotient topology.

Unit 3: 

• Connectedness : connected spaces,
• Path connected spaces,
• Connected sets in the real line,
• Components and path–components,
• Locally connected spaces and path connected spaces.

Unit 4: 

• Compactness: compact spaces,
• Compact sets in the real line, 
• Limit–point compactness,
• Locally compact spaces,
• One–point compactificaton.

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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