MT4526 Topology

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

10.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof C P Bleak

Prof C P Bleak
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Collin Bleak

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module introduces the ideas of metric and topological spaces. A metric space is simply a set together with a 'distance' between any two points. This idea is pervasive in mathematics: from situations such as the usual distance in n-dimensional space, to the Hamming distance between words in an error-correcting code and the distance between functions approximating a given function. Metric spaces can be thought of as particular instances of topological spaces, where the fundamental concept is that of points being 'close' to each other rather than the precise distance between points. Topological spaces are a powerful generalisation of metric spaces, and have had a profound influence in the development of mathematics. Many examples of metric spaces and topological spaces will be introduced and fundamental ideas within topology will be discussed, including separation axioms, compactness and connectedness.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3502

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Be able to define the concept of a topological space and continuous maps between them, and how to spot topological spaces arising in diverse settings, including analysis, algebra, and combinatorics.  they will demonstrate this by applying topological ideas and results to unseen problems
  • Know how to construct new topological spaces from existing ones as subspaces, products, and quotients, and treat algebraic objects such as groups or vector spaces as topological spaces
  • Use the notions of compactness and connectedness to generalise basic results from calculus to much larger classes of spaces.  they will be able to give the definitions surrounding and proofs of results such as the Extreme Value Theorem and Uniform Continuity Theorem
  • Be able to differentiate  between a metric properties and topological ones, and be able to prove that a topology does not arise from a metric using several techniques, including separation properties and basis cardinality arguments