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MA30055: Introduction to topology

Follow this link for further information on academic years Academic Year: 2015/6
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Honours (FHEQ level 6)
Further information on teaching periods Period: Semester 2
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment: MA30055 Mandatory Extra Work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA30041
Further information on descriptions Description: Aims & Learning Objectives:
Aims:
To provide an introduction to the ideas of point-set topology culminating with a sketch of the classification of compact surfaces. As such it provides a self-contained account of one of the triumphs of 20th century mathematics as well as providing the necessary background for the level 4 unit in Algebraic Topology.
Objectives: To acquaint students with the important notion of a topology and to familiarise them with the basic theorems of analysis in their most general setting. Students will be able to distinguish between metric and topological space theory and to understand refinements, such as Hausdorff or compact spaces, and their applications.

Content:
Topics will be chosen from the following: Topologies and topological spaces. Subspaces. Bases and sub-bases: product spaces; compact-open topology. Continuous maps and homeomorphisms. Separation axioms. Connectedness. Compactness and its equivalent characterisations in a metric space. Axiom of Choice and Zorn's Lemma. Tychonoff's theorem. Quotient spaces. Compact surfaces and their representation as quotient spaces. Sketch of the classification of compact surfaces.
Further information on programme availabilityProgramme availability:

MA30055 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
  • USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
  • USCM-AFB01 : BSc Computing (Year 3)
  • USCM-AKB01 : BSc Computing with Year long work placement (Year 4)
Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • TSMA-AFM09 : MSc Mathematical Sciences
  • TSMA-APM09 : MSc Mathematical Sciences
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
Department of Physics
  • USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
  • USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
  • USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
  • USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
  • USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.