Page 176 - DMTH401_REAL ANALYSIS

Real Analysis

Notes (iii) f(x) = Cx, " x R where C is a fixed constant.
(iv) f(x) = x, g(x) = sin x, " x R

Both f(x) and g(x) are uniformly continuous but their product
f(x) g(x) = x sin x
is not uniformaly continuous on R.

2. (i) True (ii) True
(iii) False (iv) True
(v) True (vi) False
(vii) False (viii) True
(ix) False (x) True

12.6 Further Readings

Books Walter Rudin: Principles of Mathematical Analysis (3rd edition), Ch. 2, Ch. 3.
(3.1-3.12), Ch. 6 (6.1 - 6.22), Ch.7(7.1 - 7.27), Ch. 8 (8.1- 8.5, 8.17 - 8.22).
G.F. Simmons: Introduction to Topology and Modern Analysis, Ch. 2(9-13),
Appendix 1, p. 337-338.
Shanti Narayan: A Course of Mathematical Analysis, 4.81-4.86, 9.1-9.9, Ch.10,Ch.14,
Ch.15(15.2, 15.3, 15.4)
T.M. Apostol: Mathematical Analysis, (2nd Edition) 7.30 and 7.31.
S.C. Malik: Mathematical Analysis.
H.L. Royden: Real Analysis, Ch. 3, 4.

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