Faculty of Science

Model (No 12)

Course Specification : توبولوجى (1)

2010 - 2011

Farabi Quality Management of Education and Learning - 21/11/2024

University :Mansoura University

Faculty :Faculty of Science

Department :

1- Course data :-

2- Course aims :-

3- Course Learning Outcomes :-

4- Course contents :-

No	Topics	Week
1	? Basic Constructions.Metric spaces: Definition and examples. Open sets and neighbourhoods. Introduction to topological spaces: From the general notion of the distance in the theory of metric spaces to the definition of topological spaces, examples, open sets, and closed sets
2	? Operations on topological spaces: Neighbourhood systems, bases and subbases. Interior, closure, derived set.
3	? Continuity: Continuous mapping, open mapping, closed mapping, homeomorphisms, topological and non-topological properties.
4	Separation axioms
5	? Building new spaces from old: Subspace, quotient by equivalence relations and product topologies.
6	? Compactness: Definition using open covers, examples, closed subsets of compact spaces, compact subsets of a Hausdorff space, the compact subsets of the real line, continuous images of compact sets, . Quotient spaces and the product of two compact spaces.

5- Teaching and learning methods :-

S	Method
	Three hours lecture weekly with exercise sheets and solution sheets
	Weekly one hour tutorials in groups
	Using Internet facilities

6- Teaching and learning methods of disables :-

Science students are usually normal. Therefore, no specific teaching and learning methods are needed.

7- Student assessment :-

A. Timing

No	Method	Week
1	Oral exam	14
2	Final exam	15

B. Degree

8- List of books and references

S	Item	Type
1	Lipschutz, S. General Topology, Schaum`s outline series.
2	James R. Munkres, Topology, A First Course, Prentic Hall of India (1988)
3	http://en.wikipedia.org/wiki/Topology
4	K. D. Joshi, Introduction to General topology, New Delhi, Wiley Eastern Limited, 1983.
5	W. J. Porvin, Foundation of General topology, New Yourk, Academic press 1965.
6	H. Seifert and W. A. Threlfall, A texetbook of topology. New York, Academic press, 1980
7	James R. Munkres, Topology, 2nd ed., Upper Saddle River, NJ: Prentice-Hall, 2000.

9- Matrix of knowledge and skills of the course

S	Content	Study week
	? Basic Constructions.Metric spaces: Definition and examples. Open sets and neighbourhoods. Introduction to topological spaces: From the general notion of the distance in the theory of metric spaces to the definition of topological spaces, examples, open sets, and closed sets
	? Operations on topological spaces: Neighbourhood systems, bases and subbases. Interior, closure, derived set.
	? Continuity: Continuous mapping, open mapping, closed mapping, homeomorphisms, topological and non-topological properties.
	Separation axioms
	? Building new spaces from old: Subspace, quotient by equivalence relations and product topologies.
	? Compactness: Definition using open covers, examples, closed subsets of compact spaces, compact subsets of a Hausdorff space, the compact subsets of the real line, continuous images of compact sets, . Quotient spaces and the product of two compact spaces.

Course Coordinator(s): -

Head of department: -

Ahmed Habeb Mohamed Nageb Elbassiony