MAT 302 ANALYSIS II Examen 2024

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. 2.

   Show that every closed subset of a complete metric space is complete. [3 marks]