Stone spaces and compactifications

Abstract

This paper deal with spaces such that their compactification is a Stone space. The particular cases of the one-point compactification, the Wallman compactification and the Stone-Čech compactification are studied.Mathematics Subject Classification: 06B30, 06F30, 54F05

Scattered Spaces, Compactifications and an Application to Image Classification Problem

“…Compact scattered spaces have found important use in analysis and topology (see for example [10] in which S. M r o w k a, M. R a j a g o p a l a n, T. S o u n d ar a r a j a n characterized compact scattered Hausdorff spaces). On the other hand, from 2004 to 2015 K. B e l a i d et al [1], [4], [5] studied some topological spaces and compactifications. Section 2 is devoted to a short study of digital spaces and to a characterization of the subspace A to get its closure scattered.…”

On Khalimsky topology and applications on the digital image segmentation

“…More precisely, the fact that, the topological gradient approach do not give necessary closed contours make the results of the segmentation process not suitable enough. On the other part, from 2004 to 2013 K. Belaid et al [4,5,6,1] have studied some topological spaces and compactifications. More precisely, let Y be a topological space and let X be a subset of Y. Y is said to be a compactification of X, if the following properties are verified:…”