Whenever editing is allowed on the nLab again, this article should be ported over there.

Definition

In set theory

Let $S$ be a sequential convergence space. Then $S$ is a sequentially Hausdorff space if for all sequences $x \in S^\mathbb{N}$, the set of all limits of $x$ has at most one element

$isSequentiallyHausdorff(S) \coloneqq \forall x \in S^\mathbb{N}. \{l \in S \vert isLimit_S(x, l)\} \cong \emptyset \vee \{l \in S \vert isLimit_S(x, l)\} \cong \mathbb{1}$

where $\mathbb{1}$ is the singleton set.

One could directly define the limit $\lim_{n \to \infty} (-)(n)$ as a partial function