Synopsis:

• This course is an introduction to point-set topology. We will begin by discussing metric spaces. After seeing a number of reasons why the notion of metric space is not quite as general as one might like, we will delve into the more general notion of topological space. We will discuss important properties of spaces, including compactness, connectedness, and separation properties. Standard constructions for spaces, like products and quotients, will also be covered.
  
  This course is the first (of two) semesters of the Topology Prelim sequence.

Texts:

• Topology, 2nd ed., James Munkres (expensive)
• General Topology, Stephen Willard (cheap)
• Intro to Topological Manifolds, John M. Lee (available online)

Test dates (estimate):

• Test 1: Friday, Oct. 10,
• Test 2: Monday, Nov. 17,

Final exam: Wednesday, Dec. 17, 3:30PM-5:30 PM

Homework: Homework exercises will be assigned to complement the material in the lectures and collected every Friday. You are strongly encouraged to work in groups on the homework, but you must write up your solutions independently. There will be no homework due the week of an exam.

Grading policy: The breakup will be: Homework - 25%, Midterm I - 25%, Midterm II - 25% , Final exam - 25%.