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