#Contents# * table of contents {:toc} ## Idea ## The most general space where the notion of convergence and limits of sequences make sense. ## Definition ## ### In set theory ### A set $S$ is a __sequential convergence space__ if it comes with a [[binary relation]] $isLimit_S(-,-)$ between the sequence set $\mathbb{N} \to S$ and $S$ itself. ### In homotopy type theory ### A type $S$ is a __sequential convergence space__ if it comes with a [[binary relation]] $isLimit_S(-,-)$ between the sequence type $\mathbb{N} \to S$ and $S$ itself. ## See also ## * [[limit of a sequence]] * [[sequentially Hausdorff space]]