MAT 302 ANALYSIS II CA 2016
About this paper
MAT 302: Test II for MAT302 Analysis II, Department of Mathematics, Faculty of Science, University of Buea, 4 June 2016 (topology-focused paper). Exercise 1: definitions of open set, closed set, adherent point, metric subspace, dense set, closure, continuity; proofs that d(x,A)=0 iff x is in the closure of A, and that d(x,A)=d(x, closure of A). Exercise 2: characterizations of continuity, the agreement set of two continuous functions being closed, and a dense-agreement-implies-everywhere-equal argument. Exercise 3: for disjoint closed sets A, B, constructing a continuous separating function g(x)=d(x,A)/(d(x,A)+d(x,B)) and using it to build disjoint open sets separating A and B.
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University of Buea
Faculty of Science - FS
Mathematics - MAT
ANALYSIS II
CA · Second Semester · Level 300
From this paper
- 1.
In a metric space (X, d), carefully define the following: Open set, Closed set, Adherent point, Metric subspace, Dense set, Closure of a set, Continuous function. (7 marks)
- 1.
State, without proof, three different characterizations of continuity. (3 marks)
At a glance
- Course code
- MAT302 (MAT 302)
- Type
- CA
- Year
- 2016
- 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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