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].

Me! i'm really confused the isosceles trapezoids, abcd and efgh, are similar quadrilaterals. the scale factor between the trapezoids is 2: 3, line gh = 6 centimeters, line ad = 8 centimeters, and line ab is three times the length of line dc . use complete sentences to answer the following prompts and include all of your calculations in your final answer. a. write a similarity statement for each of the four pair of corresponding sides. b. write a congruence statement for each of the four pair of corresponding angles. c. determine the perimeter for each of the isosceles trapezoids.