MATH 4530 Topology. HW 1 Solution
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MATH 4530 Topology. HW 9
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MATH 4530 Topology. Prelim II, Solutions
TAKE HOME
1. Degree
Let S 1 := cfw_e2i C. We define the degree of a continuous map S 1 S 1 as follows. Let x0 S 1 and
let be a path from 1 S 1 to x0 .
(1) Sho
MATH 4530 Topology. HW 4
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MATH 4530 Topology. HW 9 solutions
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MATH 4530 Topology. HW 7
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MATH 4530 Topology. HW 6 solutions
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MATH 4530 Topology. HW 10
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MATH 4530 Topology. HW 5
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MATH 4530 Topology. HW 9
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MATH 4530 Topology. HW 4 Solutions
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MATH 4530 Topology. HW 5 solutions
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MATH 4530 Topology. Prelim I Solutions
In class 75min: 2:55-4:10 Thu 9/30.
Problem 1: Consider the following topological spaces:
(1) Z as a subspace of R with the finite complement topology
(2) [0, ]
MATH 4530 Topology. Practice Problems For Final Part II solutions
(1) (One point compactification) Assume that X is a non-compact connected Hausdorff space in which
every point has a compact neighborh
MATH 4530 Topology. Practice Problems For Final solutions
Write the proofs in complete sentences.
(1) Apply Theorem 12.6 [L] (See also Remark 12.7 [L], Theorem 72.1 [M]) and compute the fundamental gr
MATH 4530 Topology. HW 2 Solutions
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MATH 4530 Topology. HW 3 Solution
(1) Show that X is a Hausdorff space if and only if the diagonal := cfw_(x, x) | x X X X is closed
with respect to the product topology.
Solution:
: Assume that the d
MATH 4530 Topology. HW 8 solutions
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MATH 4530 Topology. HW 10 solutions
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MATH 4530 Topology. Prelim I
In class 75min: 2:55-4:10 Thu 9/30.
Problem 1 (45pts): Consider the following topological spaces:
(1) Z as a subspace of R with the finite complement topology
(2) [0, ] as
MATH 4530 Topology. HW 6
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MATH 4530 Topology. HW 2
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MATH 4530 Topology. HW 1
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Fall 2010 MATH 4530 Topology. FINAL EXAM
2hr 30min: 9:00-11:30 Tue 12/14 2010.
Closed Book, 6 problems, total 105 points (5 points bonus!).
(1) (24 pts) True or False. Dont need to explain. Just say T
MATH 4530 Topology. HW 8 solutions
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Topology Math 4530
Solutions to set 2
4. (a) We must verify that (i) For all k Z there exists some S (a, b)
so that x S (ab) and (ii) that given x S (a, b) S (c, d) there is
some S (e, f ) S (a, b) S
Topology Math 4530
Solutions to set 1
4. (a) We will check that O satises the denition for topology.
i) , X O. This is given.
ii) Closure under union. An open ray A = (a, ) is characterized by
the pro
Math 453 - Prelim 1- Due Thursday Oct. 4, 4:10 pm, 2007 The rules for this exam are the same as for written HW exercises. No outside help, including other texts, people or the web. You are free to con
Math 4530 First Midterm Exam Brief solutions
1. (a) It suces to show that if a and b are in X then there is a path from f (a) to f (b) in f (X ).
Well, as X is path connected, there is a path : [0, 1]