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Main
UQU Programs
Mathematics

Topology

MTH4311
3 hours English

Topology

Topology
MTH3302 Real Analysis 1
3 hours One requisite
1 Topological Spaces: Definitions, properties and examples. / Basis, subbasis and subspace topology
2 Closed sets and limit points. / Neighborhood, base for the neighborhood system of a point (theorems- examples)
3 Limit Points, Adherent Points and derived Sets. / Housdorff Spaces. / Closure, Interior and Exterior
4 Separable Spaces. / Sub-spaces. / Finite Product of Topological Space
5 Continuity: Definitions, properties and examples. / Homeomorphism
6 Classification of continuous functions
7 Topological Equivalence / Topological and Hereditary properties
8 Others: Revision and activities, Exam, quizzes
1.1 Mapped to: K1

develop knowledge on the concept of a topology on a non-empty set and show familiarity with a different example of topological spaces.

Teaching Strategy Lectures
Assessment Methods Homework Exam-Quiz
1.2 Mapped to: K1

understand concepts such as open and closed sets, interior, closure and boundary.

Teaching Strategy Lectures
Assessment Methods Homework Exam-Quiz
1.3 Mapped to: K2

acquire in-depth knowledge of continuous, open and closed mappings between topological spaces.

Teaching Strategy Lectures
Assessment Methods Homework Exam-Quiz
2.1 Mapped to: S5

apply mathematical techniques and theorems to use continuous functions and homeomorphisms to examine the structure of topological spaces.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
2.2 Mapped to: S5

apply logical reasoning to analyze and develop mathematical proofs of metric spaces to prove the ''metrizability'' of a topological space.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
2.3 Mapped to: S6

Demonstrate the ability to generate a topology from a collection of subsets under certain conditions and without any conditions.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
3.1 Mapped to: V1

Show the ability to work independently and within groups.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
3.2 Mapped to: V2

Demonstrating communication skills and time management.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
Assessment
Weight
Midterm Exam
30%
Homework, Quizzes and Assignments
20%
Final Exam
50%
Total
100%