Topology: An Inquiry-Based Approach

Focus Questions

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  What does it mean for a set to be closed in a topological space?
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  What important properties do closed sets have in relation to unions and intersections?
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  What is a sequence in a topological space?
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  What does it mean for a sequence to converge in a topological space?
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  What is a limit of a sequence in a topological space?
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  What is a limit point of a subset of a topological space? How are closed sets related to limit points?
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  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?
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  What does it mean for a space to be Hausdorff? What important properties do Hausdorff spaces have?
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  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?