Definition
17
[0GX] Let \(E,F⊆ X\) be sets:
a point \(x_ 0 ∈ X\) is an adherent point of \(E\) if every neighborhood \(U\) of \(x_ 0\) has non-empty intersection with \(E\);
a point \(x_ 0 ∈ E\) is isolated in \(E\) if there exists a neighborhood \(U\) of \(x_ 0\) such that \(E ∩ U = \{ x_ 0 \} \);
(Note that, in some cases, sets can have at most a countable number of isolated points: see [0T4] and [0MF], and also [0T5]).