---- > [!definition] Definition. ([[finite intersection property]]) > A collection $\mathscr{C}$ of subsets of a set $X$ is said to have the **finite intersection property** if every finite subcollection $\{ C_{1},\dots,C_{n} \} \subset \mathscr{C}$ > has nontrivial intersection: $C_{1} \cap\dots \cap C_{n} \neq \emptyset$. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```