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1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U open in R2? Is...

1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U open in R2? Is it open in R1? Is it open as a subspace of the disk D={(x,y) in R2 | x^2+y^2<1} ?

2. Is there any subset of the plane in which a single point set is open in the subspace topology?

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