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Contents

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