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Chapter 13 Closed Sets in Topological Spaces
Focus Questions
What does it mean for a set to be closed in a topological space?
What important properties do closed sets have in relation to unions and intersections?
What is a sequence in a topological space?
What does it mean for a sequence to converge in a topological space?
What is a limit of a sequence in a topological space?
What is a limit point of a subset of a topological space? How are closed sets related to limit points?
What is a boundary point of a subset of a topological space and what is the boundary of a subset of a topological space? How are closed sets related to boundary points?
What does it mean for a space to be Hausdorff? What important properties do Hausdorff spaces have?
What are the separation axioms \(T_1\text{,}\) \(T_2\text{,}\) \(T_3\text{,}\) and \(T_4\text{.}\) What is the underlying idea behind these properties?
