Editing Stone–Čech compactification (section)

== History ==

[[Andrey Nikolayevich Tikhonov]] introduced completely regular spaces in 1930 in order to avoid the pathological situation of [[Hausdorff space]]s whose only continuous [[real number|real]]-valued functions are constant maps.{{sfn | Narici|Beckenstein | 2011 | p=240}}

In the same 1930 article where Tychonoff defined completely regular spaces, he also proved that every [[Tychonoff space]] (i.e. [[Hausdorff space|Hausdorff]] completely regular space) has a Hausdorff [[Compactification (mathematics)|compactification]] (in this same article, he also proved [[Tychonoff's theorem]]). 
In 1937, Čech extended Tychonoff's technique and introduced the notation ''βX'' for this compactification. 
Stone also constructed ''βX'' in a 1937 article, although using a very different method. 
Despite Tychonoff's article being the first work on the subject of the Stone–Čech compactification and despite Tychonoff's article being referenced by both Stone and Čech, Tychonoff's name is rarely associated with ''βX''.{{sfn | Narici|Beckenstein | 2011 | pp=225-273}}