Define A = {(x,y) in R^2 : x^2+y^2 <= 4 and y >= x} U {(2,2)}.

a) Is A open?

b) Is A closed?

c) What is int A?

d) What is ext A?

e) What is bd A?

f) Is A bounded?

g) Is A a compact subset of R^2?

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- Mar 18th 2007, 07:27 PMtttcomraderCompact subset problem
Define A = {(x,y) in R^2 : x^2+y^2 <= 4 and y >= x} U {(2,2)}.

a) Is A open?

b) Is A closed?

c) What is int A?

d) What is ext A?

e) What is bd A?

f) Is A bounded?

g) Is A a compact subset of R^2? - Mar 19th 2007, 04:22 PMCaptainBlack
No, there are points in A for which every neighbourhood of the point contains

points not in the set.

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b) Is A closed?

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c) What is int A?

{(x,y): x^2+y^2<4, and y>x}

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d) What is ext A?

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e) What is bd A?

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f) Is A bounded?

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g) Is A a compact subset of R^2?

RonL