Προβολή πηγαίου κώδικα για τη σελίδα Elements of General Topology (MAE513)

[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]

=== General ===
{| class="wikitable"
|-
! 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 ===
{| class="wikitable"
|-
! 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 ===
{| class="wikitable"
|-
! 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
|
{| class="wikitable"
! Activity
! Semester Workload
|-
| Lectures (6x3)
| 18
|-
| Seminars (7x3)
| 21
|-
| Individual study
| 78
|-
| Exercises/projects
| 33
|-
| Course total 
| 150
|}
|-
! Student Performance Evaluation
|
Greek or English
<br/>
Public presentation
<br/>
Final written exam
<br/>
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