Assignments from March and April, and all extra credit
problems, may be found
here.
Assignments for Math 534, January and February
First homework, due January 22
Page 10-11,
exercises 1 (c) (d) (e), 2 (h) (i), 6,
9 (b) (c) (d)
Note: For exercise 6, all you need to do is write out the proof that
A = B implies A^c = B^c in a natural way. You may use either the
book notation or the {}^c notation.
Second homework, due January 26
-
Page 11, exercises 4 (b) (d), 8, 9 (f) (g)
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Rewrite the book proof of one half of 1.2.16 using {}^c notation.
Third homework, due February 2
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Page 14, exercises 1, 2, 6, 7.
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Page 20: Find the ranges in exercise 1, and do exercise 2, also showing
those functions to be one-to-one that are one-to-one.
Fourth homework, due February 5
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Exercises 1.3, no. 4
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Exercises 1.4: 4, 5, 9.
Fifth homework, due February 9
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Exercises 1.5:
1 bc, 2 bc.
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Exercises 2.1: 1 deh and 8.
Sixth homework, due Wednesday, February 14
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Exercises 1.5: number 3
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Exercises 2.1: number 4
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Exercises 2.2: numbers 1, 2, 9
Seventh homework, due Monday, February 19
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Exercises 1.3: number 7
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Exercises 2.2: numbers 4, 5
Eighth homework, due Wednesday, February 28
Exercises 2.3: numbers 1, 2, [postponed from February 19] 4 and 9.
[Also postponed from February 19:] Show that every open set in
( R, H ) (the Sorgenfrey line)
is a union of intervals of the form [a, b).
Call a topological space a door space if every subset is either
open or closed--in some cases, both. [Terminology is due to J.L. Kelley,
ca. 1955.] Show that both the particular point topology and the excluded
point topology (page 36, numbers 3 and 4) are door spaces.