If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact.
how can i prove this?
The unioin of two finite collections is a finite collection.
Any open cover for $\displaystyle S_1\cup S_2$ is a cover for each.
So there is a subcover for each. Their union covers $\displaystyle S_1\cup S_2$.
The unioin of two finite collections is a finite collection.
Any open cover for $\displaystyle S_1\cup S_2$ is a cover for each.
So there is a subcover for each. Their union covers $\displaystyle S_1\cup S_2$.