### Characterization of $E\mathcal{F}$-subcompactification

For extending the notion of $E$-algebra, as defined in [2], we present an example of an m-admissible algebra which is not an $E$ - algebra. Then we define $E$-subcompactification and $E\mathcal{F}$-subcompactification to study the universal $E$-subcompactification and the universal $E\mathcal{F}$-subcompactification from the function algebras point of view.