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].

Determine the number of outcomes in the event. decide whether the event is a simple event or not. upper a computer is used to select randomly a number between 1 and 9 comma inclusive. event upper b is selecting a number greater than 4. event upper b has nothing outcome(s). is the event a simple event? (yes or no) because event upper b has (fewer than, exactly, more than) one outcome.

Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.71 with a standard deviation of $0.10. using chebyshev's theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.41 and $4.01? round your answer to one decimal place.

You are choosing between two health clubs. club a offers membership for a fee of $ 28 plus a monthly fee of $ 20. club b offers membership for a fee of $ 20 plus a monthly fee of $ 22. after how many months will the total cost of each health club be the same? what will be the total cost for each club? in __ months the total cost of each health club will be the same.