Definition:Separated by Function

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Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $A, B \subseteq S$.

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

$A$ and $B$ may well be singleton sets $A = \set a, B = \set b$.

In this case $a$ and $b$ are separated by function if and only if $A$ and $B$ are separated (as sets) by function.

Also see

• Results about spaces separated by function can be found here.

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