Web page of Dmytro Savchuk |

# | Due on | Problems |
---|---|---|

1 | W 9/14 | Hatcher's notes: Chapter 1 (p.16): 2, 3, 5, 6, 8, 13 Bloch: 1.2.1, 1.2.3, 1.2.8(i), 1.3.1, 1.3.2, 1.3.3, 1.3.5, 1.3.7 A. Show that the intersection of an infinite family of open sets in R^n may not be open. |

2 | W 10/5 | Hatcher's notes: Chapter 2 (p.28): 1, 2, 3, 4, 5, 6 Bloch: 1.4.1, 1.4.3 (images of closed sets under closed map are closed), 1.4.6(2,3), 1.4.7, 1.5.3, 1.5.5, 1.5.7, 1.5.9 A. Let X,Y be topological spaces. Prove that {U x V: U - open in X, and V - open in Y} is a basis for a topology in X x Y. |

3 | M 10/17 | Hatcher's notes: Chapter 2 (p.28): 9; Chapter 3 (p.42): 2, 3, 4, 8, 11, 12, 14 Bloch: 1.6.1, 1.6.2, 1.6.6, 1.6.9 |

4 (REVIEW) | F 10/21 | see pdf file, and an answer key |

5 | M 11/7 | Bloch: 2.2.1, 2.2.2, 2.2.3, 2.2.6, 2.2.9, 2.2.10, 2.2.13, 2.3.1, 2.3.2, 2.3.4, 2.3.6, 2.4.1, 2.4.2, 2.4.3, 2.5.2, 2.6.2, 2.6.3 A. Where on the list in the Classification Theorem (2.6.7) is the surface P#K#T#S#P#P#T#T#S? |

6 | W 11/29 (Project). | Bloch: 3.2.1 (affine linear map is a composition of a linear map and a shift), 3.2.2, 3.2.8, 3.2.9, 3.3.1, 3.3.2, 3.3.3, 3.3.4, 3.3.7, 3.3.9, 3.4.2, 3.5.1, 3.5.2, 3.5.3, 3.5.4. |

7 | T 12/7. | Bloch: 3.7.1, 3.7.5, 3.7.6, 3.8.3, 3.8.5 |

8 (REVIEW for FINAL - no need to submit) | M 12/12 | see pdf file, and an answer key |

Updated:
December 31st, 1969

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