TY - JOUR
AU - Deses, D.
AU - Giuli, Eraldo
AU - Lowen-Colebunders, E.
PY - 2003/04/01
Y2 - 2024/07/15
TI - On complete objects in the category of T0 closure spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 4
IS - 1
SE -
DO - 10.4995/agt.2003.2007
UR - https://polipapers.upv.es/index.php/AGT/article/view/2007
SP - 25-34
AB - <p>In this paper we present an example in the setting of closure spaces that fits in the general theory on “complete objects” as developed by G. C. L. Brümmer and E. Giuli. For V the class of epimorphic embeddings in the construct Cl<sub>0</sub> of T<sub>0</sub> closure spaces we prove that the class of V-injective objects is the unique firmly V-reflective subconstruct of Cl0. We present an internal characterization of the Vinjective objects as “complete” ones and it turns out that this notion of completeness, when applied to the topological setting is much stronger than sobriety. An external characterization of completeness is obtained making use of the well known natural correspondence of closures with complete lattices. We prove that the construct of complete T<sub>0</sub> closure spaces is dually equivalent to the category of complete lattices with maps preserving the top and arbitrary joins.</p>
ER -