Let X be a topological space and let C and U be subsets of X. Define C to be closed if C contains all its limit points and

define U to be open if every point p ∈ U has a neighborhood

which is contained in U. Assuming these definitions show

that the following statements are equivalent for a subset S of

X.

i) S is closed in X;

ii) X – S is open in X;

iii) S = [S].

Ur environment is very sensitive to the amount of ozone in the upper atmosphere. the level of ozone normally found is 4.04.0 parts/million (ppm). a researcher believes that the current ozone level is not at a normal level. the mean of 2525 samples is 4.44.4 ppm with a standard deviation of 0.80.8. assume the population is normally distributed. a level of significance of 0.020.02 will be used. make the decision to reject or fail to reject the null hypothesis. answer tables