CA2024Proposed solution included

MAT 302 Civics and Ethics CA 2024

MAT 302: Test I, University of Buea, Faculty of Science, Department of Mathematics, Course MAT302 Analysis II, May 10 2024, 10:00-11:30: Question 1, defining metric space, closed set, closure, convergent sequence, Cauchy sequence and complete metric space; Question 2, proving the L2-integral function rho(f,g) is a metric on the continuous functions on [a,b], and describing point sets under the discrete metric on R; Question 3, in a general metric space (X,d), proving d(x,K)=0 iff x is in the closure of K, proving the distance-to-a-point function f(x)=d(x,a) is uniformly continuous, and proving A subset B implies closure(A) subset closure(B), and closure(A union B) = closure(A) union closure(B).

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University of Bamenda

Faculty of Science - FS

MAT3022024

Civics and Ethics

CA · First Semester · Level 200

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Let X be a set. Define the following notions: (i) Metric space on X, (ii) closed set, (iii) closure of a set, (iv) convergent sequence, (v) Cauchy sequence, (vi) Complete metric space. (6 marks)

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