Definition:Separated by Function

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Definition

Let $\left({X, \vartheta}\right)$ be a topological space.

Let $A, B \subseteq X$.


Then $A$ and $B$ are separated by function iff there exists an Urysohn function for $A$ and $B$.


$A$ and $B$ may well be singleton sets $A = \left\{{a}\right\}, B = \left\{{b}\right\}$.

In this case $a$ and $b$ are separated by function iff $A$ and $B$ are separated by function.