syllabus (html)(postscript)

22M:132:001 General Topology 3 s.h. Time & Location: 12:30P - 1:20P MWF 210 MLH

HW assignment 1:

1.) Define countable.

2.) Prove that the rationals are countable by using the definition of countable.

3.) Prove that the reals are uncountable by using the definition of countable.

4.) Prove that the irrationals are uncountable.

p83: 4, 8

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HW assignment 2: p. 91: 1, 3, 4, 6, 10

HW assignment 3: p. 91: 8 and p. 101: 6, 7, 13, 14, 15, 16

HW assignment 4: p. 101: 8 and p. 111: 1, 2, 9, 13

HW assignment 5: p. 118: 3, 5, 6, 7 and p. 126 1 or 3

HW assignment 6: [p. 126: (4, 5) or 8] and p. 152: 2, 7

HW assignment 7: p. 134: 6, 7, 10

HW assignment 8 (due 3/29) p. 145: 4, 6 and topological groups: 1, 2ae, 5a

HW assignment 9 (due 4/5) p. 152: 8; p. 158: 3, 8; p. 162: 2

HW assignment 10 (due 4/12) p. 171: 4, 5, 8, 11 and Either disprove $f: A \rightarrow B$, $f$ bijective and continuous, $A, B \subset {\cal R}$ implies $f$ is a homeomorphism or prove assuming $A$ is open in ${\cal R}$.

HW assignment 11 (due 4/19)
p. 178: 4, 6, p. 194: 1 and

1.) Limit point compactness does not implies sequential compactness.

2.) Suppose $X$ is first countable and $T_1$, then limit point compactness implies sequential
compactness.

HW assignment 12 (due 4/26) p. 181: 1, 5 and p. 186: 3, 4 and 5

HW assignment 13: 30: 16; 31: 5; 32: 4, 5 and

A subspace a of Lindelof space need not be Lindelof
(Hint: The ordered square $= [0, 1] \times [0, 1]$ with the order topology using the dictionary order).

HW assignment 14: 33:1; 43: 8, 10

TENTATIVE CLASS SCHEDULE-ALL DATES SUBJECT TO CHANGE (click on date/section
for pdf file of corresponding class material):

Monday | Wednesday | Friday | |

Week 1 | 1/21: 12, 13, 14 (ps), (pdf), | 1/23: 13 | |

Week 2 | 1/26:13, 14 , sub/neg(ps) sub2(ps) | 1/28:14, 15(ps) | 1/30: 16(ps) |

Week 3 | 2/2: 14 example (ps), 16 | 2/4: quiz 1, 16, 17(ps) | 2/6: 17cont(ps), |

Week 4 | 2/9: | 2/11: 18(ps) | 2/13: |

Week 5 | 2/16: 19(ps) | 2/18: quiz 2, 19 cont(ps) | 2/20: |

Week 6 | 2/23: 20(ps) | 2/25: 20 cont | 2/27: 21(ps) |

Week 7 | 3/1: quiz 3, 23(ps) | 3/3: 21 cont | 3/5: 23 cont |

Week 8 | 3/8: 22 | 3/10: | 3/12: 23 |

Spring Break | |||

Week 9 | 3/22: 22 | 3/24: 24 | 3/36: 25 |

Week 10 | 3/29: 25 | 3/31: 26 | 4/2: Review |

Week 11 | 4/5: Midterm | 4/7: 26, 27 | 4/9: 27 |

Week 12 | 4/12: 28 | 4/14: 29 | 4/16: 29, 30 |

Week 13 | 4/19: 30 | 4/21: 31, quiz 5 | 4/23: 32 |

Week 14 | 4/26: 32, 33 | 4/28: 33 | 4/30: 43 |

Week 15 | 5/3: 43, 46 | 5/5: 46, quiz 6 | 5/7: Review |

5/14: Final Exam 9:45 a.m. |