Let fs r be a finite set. (a) prove that f is closed (b) prove that every point in f is an isolated point.

a) Suppose that F is ordered in ascending order: . Then, the complement of F can be written as

which is the union of a finite number of open intervals, then is an open set. Thus, F is a closed subset of the real numbers.

b) Take an arbitrary element of F, let us say . Now, choose a real number such that

there are not other element of F, because is less that the minimum distance between and its neighbors.

In case that we only consider , and if we only consider .

Then, all points of F are isolated.

Step-by-step explanation:

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: