Applied General Topology - Vol 04, No 1 (2003)

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A note on separation and compactness in categories of convergence spaces
The quasitopos hull of the construct of closure spaces
On complete objects in the category of T0 closure spaces
On φ 1,2-countable compactness and filters
The local triangle axiom in topology and domain theory
Dense Sδ-diagonals and linearly ordered extensions
Holonomy, extendibility, and the star universal cover of a topological groupoid
Functorial approach structures
On the use of partial orders in uniform spaces
Effective representations of the space of linear bounded operators
Skew compact semigroups
On classes of T0 spaces admitting completions
Di-uniform texture spaces
Injective locales over perfect embeddings and algebras of the upper powerlocale monad

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On complete objects in the category of T0 closure spaces
(Universitat Politècnica de València, 2003-04-01) Deses, D.; Giuli, Eraldo; Lowen-Colebunders, E.
[EN] 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 Cl0 of T0 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 T0 closure spaces is dually equivalent to the category of complete lattices with maps preserving the top and arbitrary joins.