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].

Give the functions f(x) = |x + 2| - 3, what is the domain? a,b,c, or d all real numbers x > 2 x < -2 all real numbers and x cannot equal to 2

Val and tony get paid per project. val is paid a project fee of $44 plus $12 per hour. tony is paid a project fee of $35 plus $15 per hour. write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.

Over the course of the school year, you keep track of how much snow falls on a given day and whether it was a snow day. your data indicates that of twenty-one days with less than three inches of snow, five were snow days, while of the eight days with more than three inches of snow, six were snow days. if all you know about a day is that it is snowing, what is the probability that it will be a snow day?