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 ?
The Lipschitz condition is not satisfied at these points and different solutions can be pieced together there, allowing for compactification of the waveform.
Mathematicians at the University of Malaga in Spain examine the subtleties of both the Cauch boundary for a generalized and possible non-symmetric distance, and the Gromov compactification for any, possibly incomplete, Finsler manifold.
The study of to obtain a compactification for any space was introduced by Wallman [6].
This process is not unlike the compactification of the extra dimensions in the Kaluza-Klein and super-string theories.
Compactification of the Lorentz group in the two-world picture would be interesting.
We shall also use the idea of compactification of extra dimensions due to Klein [2].
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.
c]-ultrafilter and the compactification of a fuzzy topological space.
Topics include the Littlewood conjecture in fields of power series, series and polynomials representations for weighted Rogers-Ramanujan partitions and products modulo 6, limiting processes with dependent increments for measures on symmetric groups of permutations, the ramification of a shift by two, the dynamics associated with certain digital sequences, a new approach to probabalistic number theory through compactification and integration, low discrepancy sequences generated by dynamical systems, renormalized Rauzy functions, approximations for the Goldbach and twin prime problem and gaps between consecutive primes, eigenfunctions for substitution tiling systems, and a review of the highlights of the "marriage" of probability and number theory.
Not unlike the one-point compactification of the complex plane by adding the points at infinity leading to the Gauss-Riemann sphere.
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.