Uniform-type structures on lattice-valued spaces and frames

@article{Garca2008UniformtypeSO,
  title={Uniform-type structures on lattice-valued spaces and frames},
  author={Javier Guti{\'e}rrez Garc{\'i}a and Iraide Mardones-P{\'e}rez and Jorge Picado and Mar{\'i}a Angeles de Prada-Vicente},
  journal={Fuzzy Sets Syst.},
  year={2008},
  volume={159},
  pages={2469-2487}
}
By introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures a significant class of Hutton's uniform spaces. The categories of L-valued uniform spaces and L-valued… Expand
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