MAT 302 ANALYSIS II CA 2025
About this paper
MAT 302: Test I for MAT302 Analysis II, Department of Mathematics, Faculty of Science, University of Buea, 2 May 2025. Exercise 1: definitions of metric, open ball, convergent sequence, Cauchy sequence, complete metric space. Exercise 2: using the point-to-set distance delta(p,A)=inf{d(p,a): a in A}, proving closure characterizations, monotonicity and symmetry-type properties of delta, that G={x: delta(x,A)<delta(x,B)} is open and F={x: delta(x,A)=delta(x,B)} is closed, and separating disjoint closed sets by disjoint open sets. Exercise 3: the product (sup) metric on E1 x E2, its limit/accumulation-point behaviour, and completeness of the product given completeness of each factor.
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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 nonempty set. Define the following notions: a Metric on X, Open ball, open set, convergent sequence, Cauchy sequence, Complete metric space. [6 marks]
At a glance
- Course code
- MAT302 (MAT 302)
- Type
- CA
- Year
- 2025
- 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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