Homework 6, due Thursday, October 25, 2012
Do any 5 of the 8 problems. Each problem is worth 20 points. Solutions will be graded for
correctness, clarity and style.
(1) Let (X, dX ) and (Y, dY ) be me
Homework 4, due Thursday, September 20, 2012
Given sets X and Y , dene the product X Y to be the set X Y = cfw_(x, y ) : x X, y Y ,
and dene the projection maps X : X Y X and Y : X Y Y by X (x, y ) =
Homework 3, due Thursday, September 13, 2012
Let X be a metric space with metric d. Let S X . We say that S is bounded if for some
r > 0 and x X we have S DX (x, r).
If X is a topological space and S
Exam 2, Thursday, November 6, 2012
Do any 8 of the 13 problems. Each problem is worth 12 points. (For each True/False problem,
answer T if it is true, and if it is false, answer F and give an explicit
Homework 1 Solutions
Let X and Y be sets and let f : X Y be a mapping. Let A, B X and C, D Y be subsets, and let
Ai X , i I , be a family of subsets, indexed by some set I .
Remember: the goal in writ
Homework 2, due Thursday, September 6, 2012
Let f : X Y be a mapping of sets. We say f is one to one (or injective) if whenever x1
and x2 are in X with f (x1 ) = f (x2 ) then x1 = x2 . Another way to
Exam 1, Thursday, September 27, 2012
Do any 10 of the 14 problems. Each problem is worth 10 points. (For each True/False problem, answer T if it is true, and if it is false, answer F and give an expli
Homework 8, due Tuesday, November 27, 2012
Do any 4 of the 6 problems. Each problem is worth 25 points. Solutions will be graded for
correctness, clarity and style.
(1) Let X be a topological space an
Homework 8, due Tuesday, November 27, 2012
Do any 4 of the 6 problems. Each problem is worth 25 points. Solutions will be graded for
correctness, clarity and style.
(1) Let X be a topological space an
Homework 6, due Thursday, October 25, 2012
Do any 5 of the 8 problems. Each problem is worth 20 points. Solutions will be graded for
correctness, clarity and style.
(1) Let (X, dX ) and (Y, dY ) be me
Homework 5, due Thursday, October 11, 2012
Do any 5 of the 8 problems. Each problem is worth 20 points. Solutions will be graded for
correctness, clarity and style.
(1) Let X be a topological space. I