  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 and uniqueness 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 cis-morphisms. Moreover, the transition to
fundamental limit space can be considered a functor from this category into
category of topological spaces. Later, we show results about properties on
functors and counter-functors for inductive closed injective system and
fundamental limit spaces. We finish with the presentation of some results of
characterization of fundamental limite space for some special systems and the
study of so-called perfect properties.
