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**1. The problem statement, all variables and given/known data**

Can someone check this for me?

Problem: determine which, if any of the sets if open? closed? compact?

R=reals; Q=rationals and Z=integers.

A= [0,1) U (1,2) is NEITHER

B=Z is CLOSED

C=(.5,1) U (.25,.5) U (.125, 25) U... is OPEN

D={r*sqrt(2) such that r is an element of Q} is NEITHER

E=R-Z is OPEN

**2. Relevant equations**

How do you find the set of accumuluation points for each of the above sets?

**3. The attempt at a solution**

my reasoning:

A) the union is [0,1) -1. And [0,1) is neither open nor closed and 1 is bounded. so A is neither.

B) closed by definition?

C) union of open intervals is open

D) Q is not closed and the complement of Q is neither (none of the points in Q are interior points so Q is not open and its complement R-Q has the same property so it is not open, therefore, Q is not closed)

E) from (B), R-Z is the complement of Z, so it is open.