Uber auf-Erweiterungen
The class of ultrasmooth dendroids is contained in the class of smooth dendroids and contains the class of locally connected dendroids. In this paper we study relationships between ultrasmoothness and smoothness in dendroids and we characterize ultrasmooth dendroids.
We construct the example of the title.
We prove that a metric space is an ANR if, and only if, every open subset of X has the homotopy type of a CW-complex.
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.
For a completely regular space X, C(X) and C*(X) denote, respectively, the algebra of all real-valued continuous functions and bounded real-valued continuous functions over X. When X is not a pseudocompact space, i.e., if C*(X) ≠ C(X), theorems about uniform density for subsets of C*(X) are not directly translatable to C(X). In [1], Anderson gives a sufficient condition in order for certain rings of C(X) to be uniformly dense, but this condition is not necessary.In this paper we study the uniform...