Let be the set of all continuous functions . The mapping , where , is a homeomorphism onto its own image. Then, by definition, (where is the operation of closure). For any compactification there exists a continuous mapping that is the identity on , a fact expressed by the word "largest" .
|||E. Čech, "On bicompact spaces" Ann. of Math. , 38 (1937) pp. 823–844|
|||M.H. Stone, "Applications of the theory of Boolean rings to general topology" Trans. Amer. Soc. , 41 (1937) pp. 375–481|
|||R. Engelking, "Outline of general topology" , North-Holland (1968) (Translated from Polish)|
|||P.S. Aleksandrov, "Some results in the theory of topological spaces, obtained within the last twenty-five years" Russian Math. Surveys , 15 : 2 (1960) pp. 23–83 Uspekhi Mat. Nauk , 15 : 2 (1960) pp. 25–95|
Instead of Stone–Čech compactification one finds about equally frequently Čech–Stone compactification in the literature.
|[a1]||R. Engelking, "General topology" , Heldermann (1989)|
|[a2]||L. Gillman, M. Jerison, "Rings of continuous functions" , Springer (1976)|
|[a3]||J.R. Porter, R.G. Woods, "Extensions and absolutes of Hausdorff spaces" , Springer (1988)|
|[a4]||R.C. Walker, "The Stone–Čech compactification" , Springer (1974)|
Stone–Čech compactification. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Stone%E2%80%93%C4%8Cech_compactification&oldid=23534