1) Show that each subset of R is not compact by describing an open cover for it that has no finite subcover.

a) [1,3)

b) N

c) {x is and element of Q: 0 <= x <= 2}

2)

If S1 and S2 are compact subsets of R, prove that S1 U S2 is compact

3) Find an uncountable open cover F of R such that F has no finite subcover. Does F contain a countable subcover?

Here is what I have for problem one,let me know what you think.

1)

For (a) On = (.9, 3 - (1/n))

For (b) On = (n - (1/4), n + 1/4)

not sure on the rest