Stone-Cech compactification

Stone-Čech compactification

[¦stōn ¦chekkəm‚pak·tə·fə′kā·shən]
The Stone-Čech compactification of a completely regular space is a Hausdorff space in which the original space forms a dense subset, such that any continuous function from the original space to a compact space has a unique continuous extension to the Hausdorff space.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The symbol [beta][GAMMA] denotes the Stone-Cech compactification of a discrete infinite space [GAMMA], and [2.sup.m] denotes m-copies of the two- element discrete space 2, that is, the m-Cantor cube endowed with the product topology; thus [mathematical expression not reproducible].
Walker, The Stone-Cech Compactification, Springer, Berlin, Germany, 1974.
We regard the Stone-Cech compactification of L, denoted [beta]L, as the frame of completely regular ideals of L.
Algebra in the Stone-Cech compactification; theory and applications, 2d ed.
Assuming only the mathematical level typical to the first year of graduate school, Hindman (Howard U.) and Strauss (Leeds U.) develop the basic background information about compact right topological semigroups, the Stone-Cech compactification of a discrete space, and the extension of the semigroup operation on S to beta S.
Based on talks delivered at Ultramath 2008: Applications of Utlrafilters and Ultraproducts in Mathematics held in Pisa, Italy, the eight papers contributed to this volume explain the theorems on measure-centering ultrafilters, apply alpha-theory to stochastic differential equations, review results on the algebraic structure of Stone-Cech compactification, and describe applications of large cardinal ultrafilters in forcing.