Metric Spaces
MATH 3260/4260 (Winter 2012)
The Tietze Extension Theorem
Lemma 1 Let (X, d) be a metric space and K a nonempty closed subset of X . Suppose
f : K R is continuous, nonconstant and bounde
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 7
Due: Tuesday, March 6 - There are 2 pages in this problem set.
1. I Suppose that (X, d) is a compact metric space. Let Y = X 2 = X X and dene
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 6
Due: Tuesday, February 28 - There are 3 pages in this problem set.
1. Suppose that (X, d) is a metric space and (xn ) a sequence in X . Given t
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 5
Due: Thursday, February 16 - at the beginning of class. There are three pages in this
assignment.
1. Suppose that (X, d) is a metric space. Pro
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 4
Midterm Exam: Thursday, Feb 2
Due: Tuesday, January 31 - at the beginning of class.
Discussion: (Problems begin on page 2.)
Recall the theorem
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 3
Due: Thursday, January 26 - at the beginning of class.
Problems
1. Pages 98 102: 5 6 7 9 (Look at these questions. Im not asking for any of the
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 2
Due: Thursday, January 19 at the beginning of class.
All analysts spend half their time hunting through the literature for inequalities which t
Metric Spaces
MATH 3260/4260 (Winter 2012)
Problem Set 1
Due: Thursday, January 12 at the beginning of class.
Solve all of the problems. Submit only those problems marked with a I . One or more Fs
ind
Metric Spaces
MATH 3260/4260 (Winter 2012)
Notes on the Baire Category Theorem
Introduction
Let (X, d) be a metric space.
Denition 1 A X is
a G set in X if A =
T
Gk where each Gk is open in X .
k=1
Metric Spaces
MATH 3260 (Winter 2012)
Midterm Exam Preparation
Midterm Exam: Thursday, February 2
Part 1: This part is closed book. It is worth 30 points.
This part consists of two pages. The rst page
MATH 3260/4260
Metric Spaces
Winter 2012
Syllabus
Professor:
Oce:
Phone:
Email:
Course web site:
Jims home page:
Jims Oce Hours:
Jim Hagler
John Greene Hall 210
303.871.3310
jhagler@du.edu
http:/www.m