Elements of General Topology (MAE513)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
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)	http:/www.math.uoi.gr/GR/studies/undergraduate/cousers/513.html

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

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

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

Π. Τσαμάτος, Τοπολογία, Εκδ. Τζιόλα, Θεσσαλονίκη 2025
Χ. Καρυοφύλη και Χ. Κωνστανιλάκη, Τοπολογία Ι και ΙΙ, Εκδόσεις Ζήτη, Θεσσαλονίκη 1990
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