Math 441A, Summer 2013
Midterm
Your Name
University of Washington
Student ID #
This exam is closed books. You may use one 8.5 11 sheet of handwritten notes. You may use
both sides. You are only allowed to write down denitions and statements of theorems o
Homework 4 due Friday Oct. 28 and Homework 3 solutions
Reading: Finish 18 (continuous functions) if you havent already, then read 19. Also
read the new section online of my supplementary notes, entitled Some continuous maps
involving Euclidean space. This
Homework 4.5 NOT TO BE TURNED IN, and Homework 4 solutions
Midterm on Fri. Nov. 4! Do not turn in Homework 4.5 but treat them as warm-up
problems for the midterm (even though some are much harder than anything on the test).
Reading: 1. Metric spaces: Well
Math 441 Midterm Solutions Fall 2016
1. A = A cfw_(0, y) : 1 y 1.
2. Let U be an open subset of X Y . Since U is a union of basic open sets, it suffices
to show that the projection of any basic open set is open. But a basic open set has the form
V W with
Homework 2 solutions
1. a) This one is easiest straight from the definition of closure. Recall A is the intersection
of all closed sets containing A, and similarly for B. Any closed set containing B also contains
A, since A B. So A B.
b) Since A A B, by p
Math 441 Summer 2009: Innite Products (19)
Recall from last time:
Given an innite cartesian product of topological spaces,
X=
X ,
we dened two topologies on X:
BOX TOPOLOGY: open sets are arbitrary unions of the following basis elements:
Bbox =
U | U is
Math 441 Summer 2009: Homework 4
I. Before attempting the homework problems: Make sure you read carefully sections
14-16 of your textbook! Understand well and memorize all denitions and examples. Recall at
least one basis for each topology. Make a list of
Math 441, Introduction to Topology
Summer 2009, MWF 10:50-11:50
Alexandra Nichifor ([email protected])
Office: PDL C-326 (office hours to be announced)
Textbook: Topology, by James Munkres, second edition, 2000.
Webpage: www.math.washington.edu
Math 441 Summer 2009: Homework 8 (last!)
The following problems are due on Wednesday, August 19
From Munkres, page 171 (section 26):
Problem 2(b): If R has the topology consisting of , R, and all subsets A such that R A
is countable, is [0,1] a compact s
Math 441 Summer 2009: Homework 3
I. Read thoroughly sections 12 and 13 of your textbook. In particular:
* Make sure you memorize and understand well the denitions for:
Topology, Open set, Finer/Coarser/Comparable topologies, and Basis
* Understand well ex
Math 441 Summer 2009: Homework 7
The following problems are due on Wednesday, August 12:
From Munkres, page 152 (section 23):
Problem 4
Problem 5 (Hint: Consider Q with subspace topology)
Problem 7
Problem 11
From Munkres, pages 157-158 (section 24):
Math 441 Summer 2009: Homework 6
The following problems are due on Wednesday, August 5:
From Munkres, pages 111-112 (Section 18):
Problem 5 (modied version): Show that the subspace (a, b) of R is homeomorphic with
(0, 1), and that (0, 1) is homeomorphic
Math 441 Final Exam Info and Review:
The final exam is on Friday, August 21, 10:50-1pm, in MEB 243 (note: room is not our usual classroom!)
You may bring two 8.5x11 handwritten note sheets (double-sided if you wish).
The exam will be comprehensive. You wi
Math 441, Midterm Information
The midterm will be on Friday, 07/24, at the usual time, and in the usual classroom. It will cover the
material of the Metric Spaces handout, sections 12-18 in Munkres (only up to page 107 in section 18)
You may bring one 8.5
Math 441 Summer 2009: Homework 5
PART I
(do by Friday; collected next week, together with Part II):
Study carefully section 17
Write up solutions for the following four problems:
From Munkres, pages 100-101:
Problem 6
Problem 8 a,c
Problem 11
Problem
Math 441A, Summer 2013
Final Exam
Your Name
University of Washington
Student ID #
This exam is closed books. You may use three 8.5 11 sheets of handwritten notes. You may
use both sides. You are only allowed to write down denitions and statements on the
Homework 2, due Friday Oct. 14, and Homework 1 solutions
Reading: 17 (closed sets, limit points, Hausdorff spaces, convergent sequences etc.).
Homework: There are two groups of problems; only the first is to be turned in. The
second group doesnt need to b