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Chapter 10 Closed Sets in Metric Spaces
Focus Questions
What are boundary points, limit points, and isolated points of a set in a metric space? How are they related and how are they different?
What does it mean for a set to be closed in a metric space?
What important properties do closed sets have in relation to unions and intersections?
How can we use closed sets to determine the continuity of a function?
How are limit points related to sequences?
How are boundary points related to sequences?
What is the boundary of a set in a metric space?
How are limit points and boundary points related to closed sets?
What is the closure of a set in a metric space?
How are closed sets related to sequences?
