A note on closure spaces determined by intersections

In this work, we study a kind of closure systems (c.s.) that are defined by means of intersections of subsets of a support X with a (fixed) closed set T. These systems (which will be indicated by M(T)-spaces) can be understood as a generalization of the usual relative subspaces. Several results (referred to continuity and to the ordered structure of families of M(T)-spaces) are shown here. In addition, we study the transference of properties from the ``original closure spaces (X,K) to the spaces (X,M(T)). Among them, we are interested mainly in finitariness and in structurality. In this study of transference, we focus our analyisis on the c.s. usually known as abstract logics, and we show some results for them.