Math 490G Spring 2000

Division 01 Section 01 Tuesday - Thursday 9:00 - 10:15---REC 313

Professor Gottlieb's office hours: Wednesdays 10 - 12, MATH 730

Grader: Xiang Long; Office: Math 717; email: xlong.math.purdue.edu

TEXT: Topology by Hocking and Young, Dover

ADDITIONAL BOOKS:

Topology by Munkres

Topology by Bredon

Introduction to Topology by Gamelin and Greene

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Topics to be covered:

• Mathematical Grammer
• sets
• mappings
• equivalences
• a metric on a set
• open sets
• continuous functions
• homeomorphisms and isometries
• compactness
• connectedness
• product spaces
• quotient spaces
• homotopy
• fundamental group
• Brouwer fixed point theorem
• Borsuk--Ulam theorem
• Vector fields
• Degrees of maps

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TAKE HOME EXAM

FINAL EXAM: May 5, 2000 at 3:20 - 5:20 in REC 313. Bring your take-home Final and be prepared to discuss your work with the class.

TAKE HOME FINAL

ASSIGNMENTS

1. Munkres: Page 13; #2a-i, 3, 4, 8. Due 1/18/00.

2. Munkres: Page 13; #2 j - q, 5 , 6. Due 1/25/00

3. Munkres: Page 20; #1, 2, 6 . Due 2/1/00

4. Munkres: Page 20: 3, 4, 5. Due 2/8/00

5. Show maps into trivial spaces and out of discrete spaces are continuous. Give examples using two point spaces of non continuous maps into discrete and out of trivial spaces. Due 2/24/00

6. Hocking and Young. 1-3, 1-4, 1-5. Due 2/29/00.

7. Hocking and Young. Prove Lemma 1-10 and 1-11. Due 3/7/2000.

8. Show that a bijective map from a compact space to a Hausdorff space is a homeomorphism. Due 4/4/00.

9. Show that a metric space is normal, and that a compact Hausdorff space is normal. Due 4/6/2000.

10. Prove theorem 2-36 in H.Y. Due 4/11/00.

11. Explicitly give a homotopy of the identity map of the three dimensional sphere into the antipodal map by writing down a mathematical formula. Hint, look for a formula for the circle and then generalize to the three sphere.

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