# TOPOLOGY

MAT4TOP

2017

Credit points: 15

## Subject outline

This subject begins with a careful discussion of the various set theoretical results that are required for the subsequent material. This is followed by a discussion of the theory of metric spaces. The most basic properties of open sets in metric spaces can be used to motivate a more generally applicable definition of open sets, which leads to the idea of a topological space.A study of fundamental concepts in the theory of topological spaces such as compactness and connectedness yields results of very general application. The subject concludes with atreatment of quotients and products of topological spaces.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorYuri Nikolayevsky

Subject year levelYear Level 4 - UG/Hons/1st Yr PG

Exchange StudentsYes

## Subject particulars

### Subject rules

Prerequisites MAT3DS OR MAT3AC

Co-requisitesN/A

Incompatible subjects MAT3TA

Equivalent subjectsN/A

Special conditionsN/A

## Graduate capabilities & intended learning outcomes

01. Read and explain highly abstract formulations in modern mathematics.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Speaking (Speaking)
Ethical Awareness (Ethical Awareness)
Writing (Writing)
Inquiry/ Research (Inquiry/ Research)
Creative Problem-solving (Creative Problem-solving)
Critical Thinking (Critical Thinking)
Discipline-specific GCs (Discipline-specific GCs)

02. Implement basic ideas in point set topology, particularly connectedness and compactness, in basic proofs.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)
Speaking (Speaking)
Writing (Writing)
Inquiry/ Research (Inquiry/ Research)
Discipline-specific GCs (Discipline-specific GCs)

03. Produce new topological spaces from given ones using the topological constructions of products and quotients.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)
Speaking (Speaking)
Writing (Writing)
Inquiry/ Research (Inquiry/ Research)
Critical Thinking (Critical Thinking)

04. Communicate mathematical arguments clearly and succinctly in the form of a written mathematical proof.

Activities:
Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
Writing (Writing)
Inquiry/ Research (Inquiry/ Research)
Speaking (Speaking)
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)

## Subject options

Select to view your study options…

Start date between: and    Key dates

## Melbourne, 2017, Semester 2, Day

### Overview

Online enrolmentNo

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorYuri Nikolayevsky

### Class requirements

Lecture Week: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.