Elements of General Topology (MAE513)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




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


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.

General Competences
  • Analysis and synthesis of data and information
  • Working independently
  • Team work
  • Working in an interdisciplinary environment
  • Production of free, creative and inductive thinking
  • Production of new research ideas


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



Use of Information and Communications Technology

Use of special software (tex, mathematica, e.t.c.) for presentation of projects and exercises.

Teaching Methods
Activity Semester Workload
Lectures (6x3) 18
Seminars (7x3) 21
Individual study 78
Exercises/projects 33
Course total 150
Student Performance Evaluation

Greek or English
Public presentation
Final written exam
Criteria for evaluation are posted on course's site (E-course) at the beginning of each semester.

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