Let $E$ be a denumerable set and let $\mathcal{F}$ be a collection of bounded functions. In the reading we had a compactification of $E$ with respect to $\mathcal{F}$, denoted by $\hat{E}_{\mathcal{F}}$.
Is there a name for this way of compactification? I would like to look for this in books but to do so I need a name for it.
The way to construct it was rather complicated.