Math 70700, Topology I, Fall 2012

Section: 18711

Tu 10:00 - 11:30 Room 5417
Th 10:00 - 11:30 Room 5417

Instructor:Joseph Maher
Office hours:T 11:30-12:30, Th 11:30-12:30
Phone:(718) 982-3623
Texts:Seymour Lipschutz, Schaum's Outlines, General Topology, McGraw-Hill, ISBN-10: 0071763473.
Allen Hatcher, Algebraic Topology, Cambridge University Press, ISBN 0-521-79540-0.


We will start with a review of point set topology, and discuss basic properties of topological spaces, including compactness, connectedness and separation properties. We will introduce some invariants from algebraic topology, starting with the fundamental group of a space, and develop the theory of covering spaces. We will also consider homology groups, and discuss many examples.


  • Metric spaces, topological spaces, continuity, Hausdorff condition, compactness, connectedness, product spaces, quotient spaces.

  • Fundamental group, covering spaces.

  • Homology.


  • HW1 Due Thu 13 Sep

  • HW2 Due Thu 4 Oct

  • HW3 Due Thu 18 Oct

  • HW4 Due Thu 1 Nov

  • HW5 Due Tue 27 Nov

  • HW6 Due Thu 13 Dec


These are the notes I make for class, they are probably not of much use to anyone else.