---- > [!definition] Definition. ([[nestles in|Nestling of Set Collections]]) > Let $\mathscr{A_{\text{inner}}}, \mathscr{A_{\text{outer}}}$ be collections of sets. We say **$\mathscr{A_{\text{inner}}}$ nestles in $\mathscr{A_\text{outer}}$** if for all $a \in A_{\text{outer}} \in \mathscr{A_{\text{outer}}}$ there exists $A_{\text{inner}} \in \mathscr{A_{\text{inner}}}$ s.t. $a \in A_{\text{inner}} \subset A_{\text{outer}}$. > [!justification] > Motivation comes from topology, e.g., [[open sets can be nestled into]] and many properties of a similar feeling. ---- #### ---- #### 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 > ```