Let $X$ be a subset of a topolgical space with no open points. Then $$\overline{X}=X_1\sqcup X_2\sqcup X_3\sqcup X_4\sqcup X_5$$ where $X_1$ are isolated points of $X$, $X_2$ are interior points, $X_3=X\setminus(X_1\cup X_2)$, $X_4$ are isolated points of the complement of $X$ and $X_5$ are none of the above.
Are there one-word English names for points in $X_3,X_4,X_5$ or some unions of these sets which actually appeared in the literature? Recall that the points in $\overline{X}$ are called adherent, $\overline{X}\setminus X_1$ are the limit points, and $\overline{X}\setminus X_2$ are the boundary points. But I do not know if there are names for other subsets (besides $X=X_1\cup X_2\cup X_3$).
(This should probably be Community Wiki.)
