Diagonal conditions for lattice-valued uniform convergence spaces (Q691789)

This paper is continuation of the author's studies on the so called stratified lattice-valued uniform convergence spaces [\textit{G. Jäger} and \textit{M. H. Burton}, Quaest. Math. 28, No. 1, 11--36 (2005; Zbl 1075.54003)]. The author defines a Fisher type diagonal condition and characterizes it by means of certain neighborhood operators. Moreover this condition is proved to be dual to uniform regularity defined by closures of stratified lattice valued filters [\textit{U. Höhle} and \textit{A. P. Šostak}, Dordrecht: Kluwer Academic Publishers. Handb. Fuzzy Sets Ser. 3, 123--272 (1999; Zbl 0977.54006)]. The main result of the paper has a form of an extension theorem for uniformly continuous mappings. The paper is not easy reading the more since many references are in German.