The ideal review for your general topology course More than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum’s Outlines cover everything from math to science, nursing to language.

1. Introduction to Topology Class Notes General Topology Topology, 2nd Edition, James R. Copies of the classnotes are on the internet in PDF format as given below. The 'Proofs of Theorems' files were prepared in Beamer.
2. The trace topology induced by this topology on R is the natural topology on R. (ii) Let A B X, each equipped with the trace topology of the respective superset. Then Xinduces on Athe same topology as B. The following result characterizes the trace topology by a universal property: 1.1.4 Theorem. Let (X;O) be a topological space, U Xand j: U!

Schaum s Outline of General Topology

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Continuation exam
Grades
Exam and solutions
Mock exam
Revision classes
Revision checklist
Reference group
Lecture notes
Exercise sheets
Literature guide
Timetable
Øvingstime
Introduction
Formal Details
Course Materials and Textbook
Contact Details

Continuation exam

Congratulations to the four of you who took the exam! The grades were excellent, and I am very happy to see that you all have such a good feeling for and understanding of topology!

Grades

I have now marked the exams. I am delighted with the results! The vast majority of you achieved a thoroughly deserved A or B. I am very happy to see that you have all worked so hard and have learnt so much!

Exam and solutions

English. pdf

Norsk. pdf

Nynorsk. pdf

Solutions. pdf

Thanks and good luck!

Now that the last lecture has been given, I would just like to thank all of you for your participation. It has truly been a pleasure teaching you, I have enjoyed it greatly. I'm sure that you will all do very well on the exam — I very much hope that you will do so, and wish you the best of luck!

Mock exam

The mock exam is in the same style as the real exam will be. The questions are overall perhaps slightly more difficult than those which will be asked on the real exam.

About half a question more on the real exam compared to the mock exam will be taken from the knot theory and surfaces part of the course.

Revision classes

Revision class 1. Questions and solutions. pdf

Revision class 2. Questions and solutions. pdf

A third revision class on knot theory and surfaces took place on Wednesday, 22/05.

It is very important that you understand all of the solutions from the classes, except any which are marked as non-examinable. Just let me know if not, and I will be happy to help.

Revision checklist

This has now been updated to cover the entire course.

Reference group

Reidun Persdatter Ødegaard and Therese Mardal Hagland represented you.

A third and last meeting took place after the exam.

Thanks very much to Reidun and Therese for an excellent job!

Lecture notes

Lecture 1, 15/01. pdf
Lecture 2, 17/01. pdf
Lecture 3, 22/01. pdf
Lecture 4, 24/01. pdf
Lecture 5, 29/01. pdf
Lecture 6, 31/01. pdf
Lecture 7, 05/02. pdf
Lecture 8, 07/02. pdf
Lecture 9, 12/02. pdf
Lecture 10, 14/02. pdf
Lecture 11, 19/02. pdf
Lecture 12, 21/02. pdf
Lecture 13, 26/02. pdf
Lecture 14, 28/02. pdf
Lecture 17, 12/03. pdf
Lecture 18, 14/03. pdf
Lecture 19, 19/03. pdf
Lecture 20, 21/03. pdf
Lecture 21, 04/04. pdf
Lecture 22, 09/04. pdf
Excerpts from Lectures 23 – 27. pdf

Lectures 1–14, all together. pdf

If you have any questions, or if there's anything that you do not follow, please feel free to ask me.

All the lectures on knot theory have now been uploaded, as well as all the examinable lectures from the first part of the course.

I plan to combine the remaining lectures on surfaces into one. I have uploaded a few excerpts.

If you know Latex, you are welcome to edit the source files for the lectures. For example, it is possible to make annotations. Here are the files for Lectures 1 – 14. tar

This is a tarball, which needs to be extracted. The file which needs to be compiled (with pdflatex) is 'generell_topologi.tex'.

If you have any questions on how to compile or edit the source files, please feel free to ask me.

Exercise sheets

Exercise sheet 1. pdf
Solutions. pdf

Exercise sheet 2. pdf
Solutions. pdf

Exercise sheet 3. pdf
Solutions. pdf

Exercise sheet 4. pdf

I have not yet had time to carefully proof read the solutions to Exercise Sheet 3, and a few pictures are missing. I have made them available in case they are nevertheless helpful.

Just let me know if you cannot understand any of the solutions, and I will do my best to help! If you spot a mistake, please also get in touch!

Literature guide

A list of references, with brief comments. pdf

Timetable

Spring 2013.

Lectures

Tuesday 14.15-16.00 in F4.

Thursday 12.15-14.00 in KJL3.

Øvingstime

Wednesday 15.15-17.00 in 734, Sentralbygg 2.

General Topology Kelley Pdf

Øvingstime

In the exercise classes I will discuss the exercise sheets and the lectures with you, in a more informal setting than the lectures.

Attendance is entirely optional.

Introduction

Topology is the study of topological spaces, which are of indispensable importance across mathematics, and are equally important in physics, computer science, and other disciplines.

If the idea of studying gadgets such as knots, the Möbius band, the Klein bottle, or of turning a sphere inside out, intrigues you, or if you are baffled as to how a hundred year old problem proven recently can be of a completely different flavour in three and four dimensions than in five or more, this course is where you should start!

If you have enjoyed courses in analysis, geometry, or algebra, or any combination of these, it's likely that you'll find something to your taste in topology — it's a rich and diverse subject, and further study can lead in any or all of these directions.

This course will have two goals:

1. To introduce examples of topological spaces, illustrating various phenomena, and conveying something of topology's geometric flavour.
2. To develop the foundations of topology relied upon in higher courses.

Upon successful completion of the course, you will have acquired knowledge which will open up doors to higher courses, and will have developed skills — the suppleness of mind needed to understand topological pheneomena intuitively; an ability to reason at a more abstract level than you have probably come across before; the organisation and discipline necessary to match topological intuition to abstract rigour — which will be valuable to you in your chosen career.

Introduction To General Topology Pdf

Formal details

The lectures will be given in English.

The official course description may be found here.

There are no formal pre-requisite courses, but most of the mathematics courses you have taken previously would likely be helpful in one way or another.

General Topology Willard Pdf

Course materials and textbook

Supporting materials for the course — e.g. lecture notes and exercise sheets — will be posted here.

There is no obligatory textbook — the examination will be based upon the contents of the lectures and the exercise sheets.

However, the following textbook is recommended if you are looking for a book to support the lectures. The bookstore will order 10 copies.

M.A.Armstrong, Basic Topology.

There are many other textbooks which you may find helpful. A brief guide can be found above.

Contact Details

You are welcome to contact me by email or to come to my office at any time to discuss anything from the lectures that you did not follow, or anything else.

My email address can be found here.

My office is 1248, Sentralbygg 2. On the door it says Andrew Stacey (i.e. not my name!).

Last updated at 14:28 (GMT+2), 22/08/2013.