---- > [!definition] Definition. ([[standard topology on the real line]]) > If $\mathscr{B}$ is the collection of all [[open interval]]s in the [[real numbers|real line]], $(a,b):=\{ x : a < x < b \},$ > the [[topological space|topology]] [[topology generated by a basis|generated by]] $\mathscr{B}$ is called the **standard topology on the real line**. > \ > Compare to the [[lower limit topology, upper limit topology]] and the [[K-topology on the real line]] ---- #### ---- #### 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 > ```