\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \)

Limit points and isolated points (of sets of reals), definition

Limit points

Let \( X \) be a subset of the real line. We say that \( x \) is a limit point (or cluster point) of \( X \) if [...].

Not to be confused with limit points of sequences.

Isolated points

Let \( X \) be a subset of the real line. We say that \( x \) is an isolated point of \( X \) if \( x \in X \) and [...].