TOPOLOGY

MAT4TOP

2020

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 a treatment of quotients and products of topological spaces.

School: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Yuri Nikolayevsky

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 4 - UG/Hons/1st Yr PG

Exchange Students: No

Available as Elective: No

Learning Activities: N/A

Capstone subject: No

Subject particulars

Subject rules

Prerequisites: N/A

Co-requisites: N/A

Incompatible subjects: MAT3TA

Equivalent subjects: N/A

Quota Management Strategy: N/A

Quota-conditions or rules: N/A

Special conditions: N/A

Minimum credit point requirement: N/A

Assumed knowledge: N/A

Career Ready

Career-focused: No

Work-based learning: No

Self sourced or Uni sourced: N/A

Entire subject or partial subject: N/A

Total hours/days required: N/A

Location of WBL activity (region): N/A

WBL addtional requirements: N/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

Intended Learning Outcomes

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

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

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

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

Melbourne (Bundoora), 2020, Semester 2, Day

Overview

Online enrolment: No

Maximum enrolment size: N/A

Enrolment information: N/A

Subject Instance Co-ordinator: Yuri Nikolayevsky

Class requirements

LectureWeek: 31 - 43
Two 1.00 hour lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Assessments

Assessment element	Comments	Category	Contribution	Hurdle	%	ILO*
5 fortnightly written assignments - 1500 words (300 words each)	N/A	N/A	N/A	No	30	SILO1, SILO2, SILO3, SILO4
One 2-hour written exam - 2000 words	N/A	N/A	N/A	No	50	SILO1, SILO2, SILO3, SILO4
Student classroom presentations - 1000 words	N/A	N/A	N/A	No	20	SILO1, SILO2, SILO3, SILO4