problem in set theory QN1 by logical argument verify that {a} is not open for any real number "a".
i guess the set is not open since there is no open interval about "a"
instead the set is said to be closed since any of its complement must be open.
am i correct?
QN2 GIVE TWO COUNTER-EXAMPLES WHICH SHOWS THAT THE IMAGE OF INTERSECTION OF TWO SETS IS NOT EQUAL TO THE INTERSECTION OF THEIR IMAGES 

Hint for Q2:
Must the image of a point in the intersection of two sets be in the intersection of the images of the two sets?
Must a point in the intersection of the images of two sets be the image of a point in the intersection of the two sets?
If the answers to these questions are different, then can you construct a counter-example? 
