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: .
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