Über die Einlagerung topologischer Gruppen in Kompakte
Let be a group, be the Stone-Čech compactification of endowed with the structure of a right topological semigroup and . Given any subset of and , we define the -companion of , and characterize the subsets with finite and discrete ultracompanions.
Given a free ultrafilter on and a space , we say that is the -limit point of a sequence in (in symbols, -) if for every neighborhood of , . By using -limit points from a suitable metric space, we characterize the selective ultrafilters on and the -points of . In this paper, we only consider dynamical systems , where is a compact metric space. For a free ultrafilter on , the function is defined by - for each . These functions are not continuous in general. For a...
Dans cet article, on développe, pour les espaces paracompacts, une méthode de construction analogue à la construction par récurrence sur les squelettes dans les -complexes. On l’applique à des problèmes de prolongement ainsi qu’à l’existence de fonctions canoniques dans les nerfs de recouvrements fermés.
Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.