COURSE UNIT TITLE

: INTRODUCTION TO TOPOLOGY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3049 INTRODUCTION TO TOPOLOGY COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR HALIL ORUÇ

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course aims to teach the fundamentals of point set topology and constitute an awareness of need for the topology in Mathematics. It expresses how can be recoup the distance concept of Analysis.

Learning Outcomes of the Course Unit

1   Will be able to write the definitions of a metric space, a topological space, and their fundamental concepts
2   Will be able to describe the open and closed sets of a given topological space
3   Will be able to find interior, exterior, boundary, limit, isolated and closure points of a set with respect to a given topological space
4   Will be able to derive new topological spaces from given ones
5   Will be able to discuss the continuity of a function between topological spaces
6   Will be able to discuss the connectedness and compactness concepts

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Metric spaces, open sets, closed sets, boundary of a set, neighbourhoods
2 Convergence and continuity in metric spaces
3 Topological spaces, topological space examples, interior point, exterior point, boundary point
4 Isolated points, limit points, closed sets and closure of a set
5 Base and subbase
6 Open neighbourhood systems, finer and coarser topologies
7 Continuous functions and homeomorphisms
8 Midterm
9 Subspace topology, metric topology and equivalent metrics
10 Product topology, quotient topology
11 Connected spaces, connected subspaces of a real line, local connectedness, path connectedness
12 Compactness and compact spaces
13 Compactification, countability and separation axioms
14 T0, T1, ve T2-spaces, regular and normal spaces, Uryshon's lemma, Tietze's extension theorem

Recomended or Required Reading

Textbooks:
1. Gemignani, M. C., Elementary Topology, 2nd ed., Dover, 1990, ISBN 978-0486665221
2. Munkres, J. R., Topology, 2nd ed., Prentice Hall, 2000, ISBN 978-0131816299
Supplementary Books:
3. Patty, C. W., Foundations of Topology, 2nd ed., Jones & Bartlett Publishers, 2008, ISBN 978-0763742348
4. Steen, L.A. & Seebach, J. A., Counter Examples in Topology, Dover, 1995, ISBN 978-0486687353
5. Willard, S., General Topology, Dover, 2004, ISBN 978-0486434797
6. Karaçay, T., Genel Topoloji, Seckin Yayıncılık, 2009, ISBN 978-1111354701, http://www.acikders.org.tr/course/view.php id=21
Materials:
Özçelik, Ahmet Z., Topoloji Lecture Notes

Planned Learning Activities and Teaching Methods

Lectures, Lecture notes and problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.40 + ASG * 0.10 + FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + ASG * 0.10 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

E-mail: ahmet.ozcelik@deu.edu.tr
Office : 0 232 3018585

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparations before/after weekly lectures 12 2,5 30
Preparation for midterm exam 1 25 25
Preparation for final exam 1 35 35
Preparation for quiz etc. 2 3 6
Preparing assignments 4 3 12
Final 1 2,5 3
Midterm 1 2,5 3
Quiz etc. 2 0,5 1
TOTAL WORKLOAD (hours) 167

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15433
LO.25433
LO.354333
LO.4543333
LO.55535433
LO.654353333

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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