Definition:Limit Point of Point
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Definition
Let $T = \left({S, \vartheta}\right)$ be a topological space.
Let $a \in S$.
A point $x \in S, x \ne a$ is called a limit point of $a$ if every open set $U \in \vartheta$ such that $x \in U$ contains $a$.
It can be seen that this is the same definition as for the definition of a limit point of a set, by requiring that the limit point for a point $a$ is defined as the limit point of the set $\left\{{a}\right\}$.
Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Limit Points
