학술논문
A note on closure spaces determined by intersections.
Document Type
Journal
Author
Fernández, Víctor (RA-UNSJ-IBS) AMS Author Profile; Brunetta, Cristian (RA-UNSJ-IBS) AMS Author Profile
Source
Subject
03 Mathematical logic and foundations -- 03C Model theory
03C95Abstract model theory
03C95
Language
English
Abstract
Summary: ``In this work, we study a kind of closure systems (c.s.) that are defined by means of {\it 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 {\it transference of properties} from the `original closure spaces $(X,\overline K)$' 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 {\it abstract logics}, and we show some results for them.''