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].

answer: 819.89 miles across america

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: