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].

Each of the walls of a room with square dimensions has been built with two pieces of sheetrock, a smaller one and a larger one. the length of all the smaller ones is the same and is stored in the variable small. similarly, the length of all the larger ones is the same and is stored in the variable large. write a single expression whose value is the total area of this room. do not use any method invocations.

Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? f(n+1)=f(n)+5

What’s 8y+48 and factor each expression completely