Lecture topics by day will be posted on an ongoing basis below. The Fundamental Group Section The project assignment is posted here. Reading After finishing our discussion of the Arzela-Ascoli-Frechet theorem and the compact-open topology, we will cover as many of the following topics as the remaining class time allows: The exam is open-text and open-notes, but students are not permitted to work together or to discuss any aspect of the exam with any other person.

In order to accomodate exceptional situations such as serious illness, your lowest homework score will be dropped at the end of the semester. The homework is the most important part of the course. Hway Kiong Lim E-mail: Within this text, we will focus on Part I, particularly Chapters and other portions on an as-needed basis. If X is compact, then X is limit point compact. If a space is path connected, it is connected too but not necessarily vice versa! Compact Subspaces of the Real Line Section

The notion of a metrizable topological space.

The Urysohn Lemma Section Proofs of some assertions about compact sets: The definition of the fundamental group. The Separation Axioms Section The extreme value theorem.

Any continuous bijection from a compact space to a Hausdorff space is automatically a homeomorphism. Lecture topics by day will be posted on an ongoing basis below. Subspaces of topological spaces.

## Math 440: Topology, Fall 2017

This syllabus is not a contract, hoework the Instructor reserves the right to make some changes during the semester. Behavior of open sets with respect to union and intersection.

Cartesian products and functions between sets. More examples around connectedness: Here is the exam. Homework 10 is due Monday, November Munkres’ Comments on Style. Properties of topological spaces: Examples of non-metrizable topological spaces.

# Math Introduction to Topology I

Limit Point Compactness Section More about subspaces of topological spaces, with examples. For further advice on writing your homework and project papersee: Open balls and topolofy sets in metric spaces. Topology provides the language of modern analysis and geometry. Also, in Theorem Direct Sums of Abelian Groups.

## Munkres (2000) Topology with Solutions

Both exams are closed bookclosed notes exams, with no calculators or other electronic aids permitted. Make-up quizzes will NOT be given.

The interior of a set. Closed Sets and Limit Points Section Homework 6 is due Wednesday, October 7.

This means you should try to use complete sentences, insert explanations, and err on the side of writing out “for all” and “there exist”, etc. A function between metric spaces is continuous if and only if it is sequentially continuousmeaning the image of a every convergent sequence with limit x is again convergent with limit f x. More about continuity being tpology to sequential continuity.

First examples of compact and non-compact spaces. A list of some methods for constructing compact subsets: