Consider the metric space R2 equipped with the standard Euclidean distance
d((x1,x2),(y1,y2))=(x1−y1)2+(x2−y2)2.
How many of the following subsets S⊂R2 are closed in this metric space?
- S={(x,y):x2+y2=1}
- S={(x,y):x2+y2≤1}
- S={(x,y):x∈Q,y∈Q}
- S={(x,0):x∈C}, where C⊂R is the middle-thirds Cantor set