---- > [!definition] Definition. ([[open interval]]) > If $X$ a set and lt;$ an [[strict order relation]] on $X$, and if $a<b$, we call the set $\{ x : a < x < b \} =: (a,b)$ > an **open interval in $X$**. If this set is empty, we call $a$ the **immediate predecessor** of $b$ and we call $b$ the **immediate successor** of $a$. ---- #### ---- #### 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 > ```