For each of the following sets say if it is compact or not. Give a short reason.

Question

For each of the following sets say if it is compact or not. Give a short reason. All these sets are subsets of the real line or the euclidean plane R2. In all cases the intended metric is the usual euclidean distance d(x,y)=|xy|.

a. E=[0,)E=[0,). Is E a closed subset of R? Is E compact?

b. E={1}{n/(n+2):n}

c. The parabolic segment E={(x,x^2):|x|1}

d. The set E=AB, where

A={(0,y):|y|1} and B={(x,y):0<x2,y=cos(/x)}

e. The set E=AB, where

A={(0,y):|y|<1} and B={(x,y):0<x2,y=cos(/x)}

(not the same question as the previous one—please look carefully.)

Explanation / Answer

a) E is not closed. Not bounded hence not compact

b) Bounded hence compact

c) Compact

d) Compact

e) compact

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.