MAT 302 ANALYSIS II CA 2024
About this paper
MAT 302: Test I for MAT302 Analysis II, Department of Mathematics, Faculty of Science, University of Buea, 10 May 2024. Question 1: definitions of metric space, closed set, closure, convergent/Cauchy sequence, completeness. Question 2: proving the L2 integral metric rho(f,g)=(integral of |f-g|^2)^(1/2) is a metric on C[a,b] via the Minkowski inequality, and describing the sets of points at discrete-metric distance 1, less than 1, and equal to 2 from the origin. Question 3: proving d(x,K)=0 iff x is in the closure of K, that x maps to d(x,a) is uniformly continuous, and closure monotonicity/union properties 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 Buea
Faculty of Science - FS
Mathematics - MAT
ANALYSIS II
CA · Second Semester · Level 300
From this paper
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.
At a glance
- Course code
- MAT302 (MAT 302)
- Type
- CA
- Year
- 2024
- Level
- Level 300
- Semester
- Second Semester
- Proposed solution
- Included
Where it's from
University
University of BueaFaculty
Faculty of Science - FSDepartment
Mathematics - MAT
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