The stability of the Z.2-projection onto some standard finite element spaces Vh, considered as a map in Lp and W^, 1 ^ p < oo, is shown under weaker regularity requirements than quasi-uniformity of the triangulations underlying the definitions of the Vh. 0. Introduction. The purpose of this paper is to show the stability in Lp and Wp, for 1 < p < oo, of the L2-projection onto some standard fini...

In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Gutiérrez Garćıa, T. Kubiak and J. Picado [Localic real functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. The purpose is to sh...

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 Hutt...