Typo fix.
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Let $X$ be a topological space, then the following are equivalent:
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Let $X$ be a topological space, then the following are equivalent:
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\begin{enumerate}
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\begin{enumerate}
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\item For each $x \in X$ and $A \subset X$ closed with $x \not\in A$, there exists $U \in \cn(x)$ and $V \in \cn(A)$ such that $U \cap V = \emptyset$.
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\item For each $x \in X$ and $A \subset X$ closed with $x \not\in A$, there exists $U \in \cn(x)$ and $V \in \cn(A)$ such that $U \cap V = \emptyset$.
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\item For each $x \in X$, the closed neighbourhoods of $x$ forms a fundamantal system of neighbourhoods at $x$.
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\item For each $x \in X$, the closed neighbourhoods of $x$ forms a fundamental system of neighbourhoods at $x$.
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\end{enumerate}
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\end{enumerate}
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If $X$ is a T1 space such that the above holds, then $X$ is \textbf{regular}.
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If $X$ is a T1 space such that the above holds, then $X$ is \textbf{regular}.
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\end{definition}
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\end{definition}
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