CoursePlan_15132_14350.docx

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Zarqa University Instructor:

Faculty of Science Lecture’s time:

Department: Mathematics Semester:

Course title: General Topology(1) Course number: 0301361

Office Hours:

Course description:

This Course is devoted to study topological spaces in general, the standard topology for the n-dimensional Euclidean spaces, finite products of topological spaces, functions, sequences, limits, and continuity on any set.

Aims of the course: General Topology is one of the major branches of modern mathematics; this course will have three general interconnected objectives.

1. will provide a firm foundation in topology to enable the student to continue more advanced study.

2. This course hopes to expose the students to both mathematical rigor and abstraction, giving there an opportunity further to develop his mathematical maturity

Intended Learning Outcomes: (ILOs)

A.

Knowledge and Understanding A1. Concepts and Theories:

1-Define and illustrate the concept of topological spaces and continuous functions.

2- Define and illustrate the concept of product topology and quotient topology.

3- Define and illustrate the concepts of the separation axioms.

4- Define connectedness and compactness.

A2. Contemporary Trends, Problems and Research:

Serve to understanding topics in mathematics A3. Professional Responsibility:

Prove a selection of theorems concerning topological spaces, continuous functions, product topologies, and quotient topologies,

B.

Subject-specific skills B1. Problem solving skills:

Prove a selection of theorems concerning topological spaces, continuous functions, product topologies, and quotient topologies, illustrate and prove the concepts of the separation axioms.

B2. Modeling and Design:

Prove related theorems

B3. Application of Methods and Tools: Prove selection of related theorems

C.

Critical-Thinking Skills C1.Analytic skills: Assess

Classify topological spaces using separation axioms and connectedness.

C2.Strategic Thinking:

Constructing a proof of theorems.

C3. Creative thinking and innovation:

Constructing a proof of theorems and describe different examples.

D.

General and Transferable Skills (other skills relevant to employability and personal development) D1.Communication:

Answers and discuss the problems D2.Teamwork and Leadership:

Allowing the students to make teamwork for solving the problems.

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Course structures:

Wee k

Credi t Hours

ILOs Topics Teaching Procedure ^Assessment_methods

1 3 ^{A1, A2,}_{B1, B2}

Define a Topology, Closed sets, A Closer Look at the Standard Topology on R¹

Lectures, Cooperative learning and discussion

Exams and Homework’

s

2 3 _{B1, B2, C1}^{A1, A2,}

Topologies Induced by Functions, The Interior, Exterior and

Boundary of a Set, Cluster Points

Lectures, Cooperative

learning and discussion ^Homework’s^{Exams and} 3 3 _{B1, B2, A3}^{A1, A2,} Bases, Finite Product of

Topological Spaces

Exams and Homework’s

4 3 _{B1, B2, C1}^{A1, A2,} Subbases, General Products Lectures, Cooperative

learning and discussion ^Homework’s^{Exams and} 5 3 ^{A1, , B1} Defining a Continuous function Lectures, Cooperative

learning and discussion ^Homework’s^{Exams and} 6 3 ^{A1, A2,}_{B1, B2} Open functions and

Homeomorphisms

learning and discussion ^Homework’s^{Exams and} 7 3 ^{A1, A2,}_{B1, B2} The identification Topology,

Quotient spaces Lectures, Cooperative

learning and discussion ^Homework’s^{Exams and} 8 3 ^{A1, A2,}B1, B2,

C1, C2 The Separation of Axioms Lectures, Cooperative learning and discussion

9 3 ^{A1, A2,}B1, B2,

C1, C2 Hausdorff Spaces Lectures, Cooperative

learning and discussion

10 3 ^{A1, A2,}^{B1, B2,}

C1, C2 Regular and Normal Spaces Lectures, Cooperative

learning and discussion ^Homework’s^{Exams and} 11 3 ^{A1, A2,}B1, B2,

C1, C2, C3

The first Axiom of Countability,

The second Axiom of Countability Lectures, Cooperative

learning and discussion ^Homework’s^{Exams and} 12 3 B1, B2, B3^{A1, A2,}

C1, C2

Connected Spaces, More Properties of Connected Spaces

13 3 _{B1, B2, D1}^{A1, A2,} Components and Locally Connected Spaces

14 3 ^{A1, A2,}B1, B2, C1, C2, D2

Compact Spaces, More Properties of Compact Spaces, Compactness in Rⁿ

learning and discussion ^Homework’s^{Exams and} 15,

16 Final Exams

References:

A. Main Textbook: An introduction to general Topology by: Paul Long B. Supplementary Textbook(s): General Topology by: STEPHEN WILLARD Assessment Methods:

Methods Grade Date

First exam 25%

Second exam 25%

Final exam 50%

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ZU/QP10F004