Closed injective systems and its fundamental limit spaces

Abstract

In this article we introduce the concept of limit space and fundamental limit space for the so-called closed injected systems of topological spaces. We present the main results on existence anduniqueness of limit spaces and several concrete examples. In the main section of the text, we show that the closed injective system can be considered as objects of a category whose morphisms are the so-called cismorphisms. Moreover, the transition to fundamental limit space can be considered a functor from this category into the category of topological spaces and continuous maps. Later, we show results about properties on functors and counter-functors for inductive closed injective systemand fundamental limit spaces. We finish with the presentation of some results of characterization of fundamental limit spaces for some special systems and the study of the so-called perfect properties.