## MATH 340 Topology Summer 2020

Rob Thompson Hunter College

Monday--Thursday 10:00am-11:53am Room: Online

July 13-August 13, 2020

**e-mail:**
robert.thompson@hunter.cuny.edu

**Office:** http://zoom.us/my/profthompson **Hours: Generally M-Th, 2:00-3:00.**

## Exam One will be Monday, 8/3. We will cover everything we've done through Thursday, 7/30.

### This is the exam, with and without solutions:

### Here is a summary list of the topics that could be on the exam.

- Definition of a topological space, examples
- Interior, closure, boundary
- subspace, relative topology
- Continuous function, homemorphism
- Bases, subbases, courser, finer topologies
- Definition of a metric space
- Definition of first countable, second countable, separable, Lindelof.
- Definition of T_1 and Hausdorff.
- Definition of Path Connected, Connected, locally path connected, locally connected

## Here are some problems to do to get ready for the exam:

### We will had a quiz Thursday, 7/23. The topics were from Chapter 5.

Specifically,
- The definition of a topological space, open set, closed set.
- Limit points
- The closure of a set, the interior of a set, the boundary of a set.
- Subspaces, relative topology

### Here is the quiz:

### The final exam will be on Thursday, August 13, 10:00-11:53am, on Zoom.

** The Homework Assignments**

- Assignment One, should be done by Wednesday July 22:

Schaum's Outline, Chapter 4, pg. 64/39,46,52,58,64

Chapter 5, pg. 73/1,2,5,13,17,34,44,50,68,82

- Assignment Two, more from Chapter 5:

55,57,72,73,79,85,88

- Assignment Three:

Chapter 6/22,25,22,37

Chapter 7/10,19,20,41,43

Chapter 9/20,23,31,34,38

### Basic Information About the Course:

### Please Note: All summer 2020 session courses at Hunter are online.
In this course we will hold synchronous, live, online classes, using
Zoom, during the regularly scheduled time slot for the course. The
office hours will also be online. To access my Zoom meeting space go
to http://zoom.us/my/profthompson in your browser and you will be
prompted to go to your zoom app. If you do not have a Zoom app
installed you will have to do that first. You do not necessarily need
to have an account with Zoom to install and use the app. If you go into the Zoom app directly just go to
profthompson.

### Recorded Classes

**My Office:**

My office hours for the summer term will for the most part be **M-Th 12:00-1:00 pm**. However there will be a couple of days when
I have to change this, but I will announce that. You don't need to make an appointment for office hours, you can
just drop in. The Zoom address is **profthompson**.

**Texts:**

**Prerequisites:**

MATH 351 or the equivalent

**Desired Learning Outcomes:**

The student will assimilate the
definitions of basic concepts Point Set Topology (otherwise known as General Topology).
The student will learn thestatements of a number of
fundamental theorems, and will study their proofs. The student will be
doing homework problems which will involve some computations as well
as proving various facts. The majority of the assessment will consist
of written exams similar to the homework problems.

**Homework/Exams/Grades:**

There will be regularly assigned
homework, but it is not to be handed in. We will discuss homework problems in class and I will post
some solutions. There will be a short quiz around the end of the second week, two exams later in the semester,
one of which will probably be a take-home. There will be a final exam on the last day of class, August 13.
Your course grade will be based on the quiz and exams, according to the following rubric:
Quiz - 15%, Exams - 25% each, Final - 25%. In addition, *class participation** may be a factor in your grade.
*

**Topics:**

This course is an introduction to General Topology,
taught at a fairly abstract and conceptual level, with an emphasis on
definitions, theorems, and proofs. The students will be doing proofs
in the homework, as well as some computations. Here is a list of
topics we hope to cover, roughly keyed to the table of contents of Schaum's Outline.

- Chapter Five: Topological Spaces
- Chapter Six: Bases and Subbases
- Chapter Seven: Continuity and homeomorphisms
- Chapter Ten: Separation Properties
- Chapter Eleven: Compactness
- Chapter Twelve: Products
- Chapter Thirteen: Connectedness
- Chapter Fourteen: Completeness
- More if time allows