Elements of General Topology (MAE513): Διαφορά μεταξύ των αναθεωρήσεων
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=== Attached Bibliography === | === Attached Bibliography === | ||
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See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus: | |||
{{MAE513-Biblio}} |
Τελευταία αναθεώρηση της 12:25, 15 Ιουνίου 2023
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General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE513 |
Semester |
5 |
Course Title |
Elements of General Topology |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is to introduce the student to basic notions of General Topology and, in some way, to generalize already obtained knowledge on metric spaces. It is an optional course for students interested in having a background on pure mathematics. It is also attempted to broaden students horizon to mathematical structures which, even if they seem abstract, they have important applications in several branches of science. |
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General Competences |
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Syllabus
The notion of Topology. Topologies from metrics and non-metrizable topologies. Bases and subbases. Fundamental notions (open sets, closed sets, closure, interior, boundary, accumulation points). Neighborhood bases and systems. Convergence of sequences in topological spaces. Nets and convergence of nets. Continuity. Topologies from sequence of functions, product spaces. Spaces of 1 and 2 countability. Separation (T1, T2, T3, T4 spaces). Compactness of topological spaces.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||||
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Use of Information and Communications Technology |
Use of special software (tex, mathematica, e.t.c.) for presentation of projects and exercises. | ||||||||||||
Teaching Methods |
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Student Performance Evaluation |
Greek or English
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- J. L. Kelley, General Topology, D. Van Nostrand Co. Inc., Toronto 1965
- J. Dugudji, Topology, Allyn and Bacon Inc., Boston 1978
- K. D. Joshi, Introduction to General Topology, Wiley Eastern Limited, New Delhi, 1986