# Homotopy Type Theory compact connected space > history (changes)

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## Definition

A

compact connected space is a space $S$ such that for subspaces $A \subseteq S$ and $B \subseteq S$ of $S$ with canonical monic mappings $i_{A,S}:A \to S$ and $i_{B,S}:B \to S$ such that the canonical monic mapping $i_{A \cup B,S}:A \cup B \to S$ is an equivalence and the canonical monic mapping $i_{\emptyset,A \cap B}:\emptyset \to A \cap B$ is an equivalence, either $i_{A,S}$ is an equivalence or $i_{B,S}$ is an equivalence.

## References

Last revised on June 17, 2022 at 23:24:49. See the history of this page for a list of all contributions to it.