MAT 302 ANALYSIS II Examen 2018

Extrait du sujet

1. 1.

   Carefully define the following notions in the framework of metric spaces: a) Lipschitz function, b) fixed point of a map, c) convergent sequence, d) Cauchy sequence, e) Complete metric space, f) continuous functions, g) uniformly continuous function, h) pointwise convergence of sequences of functions, i) uniform convergence of sequences of functions, j) compact set. (1x8 marks)

2. 1.

   Prove that every Lipschitz map is a uniformly continuous function. (3 marks)