# Normal space

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No. Shorthand A topological space is said to be normal(-minus-Hausdorff) if ... A topological space $X$ is said to be normal(-minus-Hausdorff) if ...
1 separation of disjoint closed subsets by open subsets given any two disjoint closed subsets in the topological space, there are disjoint open sets containing them. given any two closed subsets $A,B \subseteq X$ such that $A \cap B = \varnothing$, there exist disjoint open subsets $U,V$ of $X$ such that $A \subseteq U, B \subseteq V$, and $U \cap V = \varnothing$.
2 separation of disjoint closed subsets by continuous functions given any two disjoint closed subsets, there is a continuous function taking the value $0$ at one closed set and 1 at the other. for any two closed subsets $A,B \subseteq X$, such that $A \cap B = \varnothing$, there exists a continuous map $f:X \to [0,1]$ (to the closed unit interval) such that $f(x) = 0 \ \forall x \in A$ and $f(x) = 1 \ \forall \ x \in B$.
3 point-finite open cover has shrinking every point-finite open cover possesses a shrinking. for any point-finite open cover $U_i, i \in I$ of $X$, there exists a shrinking $V_i, i \in I$: the $V_i$ form an open cover and $\overline{V_i} \subseteq U_i$.