# Unitization via “End points compactification”

We know that every compactification of locally compact Hausdorff spaces correspond to a unitization of $C^{*}$ algebras. For example the one point compactification corresponds to the minimal unitization and the Stone Chech compactification correspond to the maximal unitization "Multiplier algebra".

In this question I would like to know if something is already known for noncommutative analogy of "End points compactification" as described bellows?:(Your answers and comments are very appreciated)

http://en.wikipedia.org/wiki/End_%28topology%29

and

End point compactification for metric spaces