Lesson plan	Lesson plan
What to create	Lesson plan
Which subject	Mathematics
What topic	topology definition, open sets, closed sets
What length (min)	30
What age group	College
Include homework
Include images descriptions
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Academic Subject: Mathematics

Topic: Topology Definition, Open Sets, Closed Sets

Duration: 30 minutes

Audience: College-level students (adult learners)

Objectives:

• Understand the basics of topology and its importance in mathematics
• Define open and closed sets
• Learn the properties of open and closed sets and how they relate to each other

Materials:

• Board and chalk or whiteboard and marker
• Handouts with examples of open and closed sets
• Computers or laptops with internet access (optional)

Procedure:

Introduction (5 minutes)

• Greet the class and introduce the topic of topology
• Explain the importance of topology and its real-world applications

Definition of Topology (5 minutes)

• Define topology as the study of the properties of space that are preserved under continuous transformations
• Give examples of continuous transformations (stretching, bending, twisting)
• Explain that topology deals with the general shape of an object rather than its specific properties

Open Sets (10 minutes)

• Define open sets as subsets of a space that contain no boundary points
• Give examples of open sets (a circle with the center removed, a line segment with its endpoints removed)
• Discuss the properties of open sets (they contain all of their limit points, they are closed under union and intersection)

Closed Sets (10 minutes)

• Define closed sets as subsets of a space that contain all of their boundary points
• Give examples of closed sets (a closed interval [a,b], a rectangle with its boundary included)
• Discuss the properties of closed sets (they contain all of their limit points, they are closed under intersection and finite union)

Conclusion (5 minutes)

• Summarize the main points covered in the lesson
• Encourage students to explore topology further and apply it to other areas of mathematics

Assessment:

• Distribute handouts with examples of open and closed sets and ask students to identify them
• Alternatively, if computers or laptops are available, assign online quizzes or exercises related to topology to be completed for homework.