Functorial Properties of the Space for Stratifiable Spaces X

Abstract

In the category of stratifiable spaces and continuous mappings into itself, we bring one construction  belonging to Coty called test space, which defines a covariant functor in this category. This construction  defines a functor , which allows each stratifiable space  to be immersed in a closed manner into some other space  which is a stratifiable space with "Good" functorial, geometric and topological properties. It is shown that the functor  is a normal, open and monadic functor in this category  of stratifiable spaces and continuous mappings into itself. And also it is studied the dimensional properties of the space  for the stratifiable space , defined for each  subfunctor  of the functor  for which the dimension  satisfies the inequality: .