Weakly induced modifications of I

The aim of this paper is to study weakly induced I-fuzzy topological spaces and weakly induced modifications of I-fuzzy topologies. We give two kinds of weakly induced I-fuzzy topologies for each I-fuzzy topology and prove that I-WIFTOP is a reflective and coreflective full subcategory of I-FTOP. We also discuss some relationships between several categories

Zariski closure, completeness and compactness

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A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces

We study a category of lattice-valued uniform convergence spaces where the lattice is enriched by two algebraic operations. This general setting allows us to view the category of lattice-valued uniform spaces as a reflective subcategory of our category, and the category of probabilistic uniform limit spaces as a coreflective subcategory

On classes of T0 spaces admitting completions

[EN] For a given class X of T0 spaces the existence of a subclass C, having the same properties that the class of complete metric spaces has in the class of all metric spaces and non-expansive maps, is investigated. A positive example is the class of all T0 spaces, with C the class of sober T0 spaces, and a negative example is the class of Tychonoff spaces. We prove that X has the previous property (i.e., admits completions) whenever it is the class of T0 spaces of an hereditary coreflective subcategory of a suitable supercategory of the category Top of topological spaces. Two classes of examples are provided.Giuli, E. (2003). On classes of T0 spaces admitting completions. Applied General Topology. 4(1):143-155. doi:10.4995/agt.2003.2016.SWORD1431554