compactification


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compactification

[käm′pak·tə·fe‚kā·shən]
(mathematics)
For a topological space X, a compact topological space that contains X.
References in periodicals archive ?
If F denotes the Forgetful Functor from the Category C of Compact Hausdorff Spaces (and continuous maps) to the Category T of Topological Spaces and if X denotes an arbitrary topological space, there exists a celebrated universal arrow (e, [beta](X)) from X to F known as the Stone-Cech compactification of X.
Sundrum, "An alternative to compactification," Physical Review Letters, vol.
To prove the reverse implication, we consider the Bohr compactification semigroup [??] of the semigroup [??].
In order to do so, in the following four subsections, we shall analyze the Poincare compactification of system (1.3) in the local charts [U.sub.i] and [V.sub.i], i = 1, 2, 3.
Let X be the one-point compactification of the space Y and denote by p the unique point of the set X\Y.
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.
Also the process of soft fuzzy structure compactification using soft fuzzy T'-prefilter has been established.
Furthermore, the expression for [[OMEGA].sub.Wyler][[Q.sub.4]] is also consistent with the Kaluza-Klein compactification procedure of obtaining Maxwell's EM in 4D from pure gravity in 5D since Wyler's expression involves a 5D domain [D.sub.5] from the very start; i.
Let us now turn to the compactification y = spec [O.sub.k] [union] {p [where] [infinity]} of spec [O.sub.k].
Equation (14) depicts a contracting geodesic ball and as explained in [13-15] this is DM which is an intrinsic compactification of the elements space-time in the n-th quantum state.
Xu, Nonexistence of asymptotic GIT compactification, Duke Math.
A natural way for proving the existence of a limit cycle is to show that, in the Poincare compactification, infinity has no critical points and both infinity and the origin have the same stability.