Notes in Point Set Topology

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Published	11/14/2024	[latex]Definition: compact-open topology[/latex]
Published	11/14/2024	[latex]What can be a quick and easy argument to show that two spaces are not homeomorphic?[/latex]
Published	11/14/2024	[latex]A topological space \( X \) is said to be \textbf{closed} if ... [/latex]
Published	11/14/2024	[latex]A topological space \( X \) is called a \textbf{Hausdorff space} if ... [/latex]
Published	11/14/2024	[latex]\( X \) a topological space. Every point \( x_0 \in X \) is closed \( \iff \) ... [/latex]
Published	11/14/2024	[latex]\( X \) a topological space and \( (x_n)_{n} \) a sequence in \( X \) that converges. Can \( (x_n)_{n} \) have multiple limits? [/latex]
Published	11/14/2024	[latex]\( X \) is Hausdorff \( \iff \) ... (closed) [/latex]
Published	11/14/2024	[latex]\( X \) a topological space, \( A \subseteq X \). \( x \in X \) is called a \textbf{limit point} of \( A \) if ... [/latex]
Published	11/14/2024	[latex]A subset of a topological space is closed \( \iff \) ... (limit point) [/latex]
Published	11/14/2024	[latex]\( X \) a topological space, \( A \subseteq X \). How does the set of all limit points of \( A \) relate to the closure? [/latex]
Published	11/14/2024	[latex]A \textbf{basis} for a topology on \( X \) is ... [/latex]
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