Category Of Stratified Spaces Research Articles

Some properties of the covariant functor P: Comp->Comp of probability measures that act on categories of stratified spaces

In this article, we study the geometric and topological properties of the probability measures functor P in the category of stratified spaces and continuous mappings into itself. It is proved that the space P(X) of probability measures is a AE(S) space. Bibliography: 8 titles. Keywords: functors, probabilities measures, stratifiable spaces, huperconnected, hupergeodesic, equiconnected, petraction, neighborhood.

Injective objects in the category of stratified spaces

The paper deals with the category of stratified spaces. For this category we establish the existence of the absolute extensors and study their connection with the absolute extensors in the category of filtered spaces. To this end, we introduce and investigate the absolute extensors reflecting the properties of both the filtered category and the stratified category. We determine the contractibility property as well as the local contractibility property for the stratified absolute extensors. It is shown that the family of strata for a stratified absolute neighbourhood extensor is equicontinuously locally extendable.