BSc Mathematics SEM VI 2016 17 2016-17 Topology Of Metric Spaces Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate marks

1. Q2 (a) Attempt any One 8 marks
   • (i) K C (distance K is-closed and bounded. Show that K is sequentially
   • (ii) Let. I = x be] x x C R” (distance Euclidean). Prove that J is
   • (b) Attempt any Two questions: 12
   • (i) Let (X,d) and (Y,d') be metric spaces. If (X,d) is compact and f: X isa continuous function, then show that f(X) is a compact subset of Y
   • (ii) Show that {0} U N} is a compact subset of (R,d) where d is usual distance in R using the definition of a compact subset
   • (iii) Let (X,d) be a compact metric space and f (0,00) is continuous. Show that there exists > 0 such that f(a) > Va X that ne question: ad only it
   • (ii) B is connecte at J ectec Na
2. Q1 At a Convex nned by CamS

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