---- > [!definition]+ Definition. ([[regular topological space]]) > Let $X$ be a [[topological space]] in which singletons are [[closed set|closed sets]]. > $X$ is called **regular** if given a point $x \in X$ and a [[closed set]] $B$ disjoint from $x$, there exists disjoint open sets containing $x$ and $B$ respectively. > ![[CleanShot 2024-04-20 at [email protected]]] ^definition > [!equivalence]+ > - ![[characterization of regular spaces#^001b95]] ^equivalence ---- #### 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 > ``` #reformatrevisebatch04