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].

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.