Question: prove that the sets G={(x,y) R 2 : x 2 +y 2 <1} and H={(x,y): 0

prove that the sets G={(x,y) ∈ R 2 : x 2 +y 2 <1} and H={(x,y): 0<x 2 +y 2 <1} are open, but the set F={(x,y): x 2 +y 2 ≤1} is not open in R 2

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Discrete Mathematics and Its Applications 7th edition by Kenneth H. Rosen