| CODE | MAT5213 | ||||||||
| TITLE | General Topology | ||||||||
| UM LEVEL | 05 - Postgraduate Modular Diploma or Degree Course | ||||||||
| MQF LEVEL | 7 | ||||||||
| ECTS CREDITS | 15 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | - Compactifications (The Order in the Family of all Compactifications, Cech-Stone compactification, Alexandroff one-point compactification); - Compactness Type Properties (Locally Compact Spaces, Perfect Maps, Lindelof Spaces, Cech-complete Spaces); - Paracompact Spaces and their Characterizations (The Tamano Theorem, Collectionwise Normal Spaces); - Metrisation Theorems (The Stone Theorem, The Nagata-Smirnov Theorem, The Bing Theorem, The Moore Theorem, The Arhangelskii Theorem, The Alexandroff - Urysohn Theorem); - Disconnectedness (Hereditarily Disconnected Spaces, Zero-Dimensional and Strongly Zero-Dimensional Spaces, Extremally Disconnected Spaces); - Further Topics (Linearly Ordered Topological Spaces). Study-unit Aims: General topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology. This study-unit aims to to give a connected account of various topological concepts and various theorems related mainly with Compactness, Paracompactness and Metrisabilty that may lead young researchers comprehensively to up-to-date work in the area of General Topology. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Analyse basic techniques related with coverings of topological spaces; - Recognise various fundamental constructions in General Topology, such as the Stone-Cech and Alexandroff compactifications; - Manage such fundamental concepts as compactness, compactifications, paracompactness, connectedness and disconnectedness, metrisability. 2. Skills: By the end of the study-unit the student will be able to: - Use ideas and methods of coverings to prove fundamental results related with Metrisabilty and characterizations of Paracompactness; - Improve the handling of several topological techniques; - Be prepared to pursue advanced research problems in the area. Textbooks: - J. R. Munkres, Topology, Prentice Hall, 2nd Edition, 2000. - J. I. Nagata, Modern General Topology, Volume 33 (North-Holland Mathematical Library), Elsevier Science Publisher B.V., 1985. - R. Engelking, General Topology, revised and completed edition, Helderman Verlag, 1989. |
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| ADDITIONAL NOTES | Pre-requisite Qualifications: B.Sc. with Mathematics as a main area Follows from: MAT3219 |
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| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | David Buhagiar |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
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