regular

If X is a continuum and $p \in X$, then X is said to be regular at p provided that there is a local base $\mathcal L_p$ at p such that the boundary of each member of $\mathcal L_p$ is of finite cardinality. A continuum is said to be regular provided that X is regular at each of its points. A continuum is Regular if each two of its points can be separated by a finite point set.