MAT 302 ANALYSIS II Examen 2025

Extrait du sujet

1. Let (X, d) be a metric space. Carefully define the following notions in the framework of metric spaces: a) Open and closed sets, 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) Connected set.

2. 1.

   Carefully state, without proof, the Double Limit Theorem and the Alternating Series Test Theorem, for uniform convergence of sequences of functions and series of functions. (6 marks)