Properties:: [[singletons are a basis for the discrete topology]] Sufficiencies:: *[[Sufficiencies]]* Equivalences:: *[[Equivalences]]* ---- Let $X$ be any set. > [!definition] Definition. ([[discrete topology]]) > The [[power set]] $2^{X}$ of a set $X$ defines a [[topological space|topology]] on $X$, called the **discrete topology**. > \ > The collection consisting of $X$ and $\emptyset$ is a [[topological space|topology]] on $X$ too, called the **indiscrete topology** or **trivial topology**. ---- #### ---- #### 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 > ```