TOPOLOGY AND FUNCTIONAL ANALYSIS BHARATHIDASAN UNIVERSITY, TIRUCHIRAPPALLI – 620 024 M.Sc. MATHEMATICS SYLLABUS (ANNUAL PATTERN)

BHARATHIDASAN UNIVERSITY, TIRUCHIRAPPALLI – 620 024
M.Sc. MATHEMATICS SYLLABUS (ANNUAL PATTERN)
(FOR DISTANCE EDUCATION CANDIDATES ONLY)
(For the candidates admitted from the academic year 2006-2007 batch onwards)
PAPER VI – TOPOLOGY AND FUNCTIONAL ANALYSIS

Unit I
Topological spaces and continuous functions – Product topology – metric topology – The metric topology (continued) – connectedness.

Unit II
Compactness – Count ability axioms and Separation axioms.

Unit III
The Tychonoff theorem – Completer metric spaces and Function spaces

Unit IV
Banach spaces

Unit V
Hilbert spaces – finite dimensional spectral theory.

TEXT BOOK:

1. James R. Munkres, “Topology – A First Course”, PHI (Second edition)
Unit 1: Chapter 2 (Sec 2.1 to 2.10)
Chapter 3 (Sec 3.1 to 3.4)
Unit II: Chapter 3 (Sec 3.5 to 3.7)
Chapter 4
Unit III: Chapter 5
Chapter 7 (Sec 7.1 to 7.3)
Functional Analysis

Text Book
1. G.F. Simmons, “Introduction to Topology and Modern Analysis”, Mc-Graw Hill. 1963
Unit IV: Chapter 9.
Unit V : Chapter 10 and 11.

References:
1. J. Dugundji, “Topology”, PHI, New Delhi, 1975
2. Goffman and Pedrick, “First course in Functional Analysis”, PHI
3. B.V. Limays, “Functional Analysis”, Wiley Eastern.