论文信息 - A note on regularity

A note on regularity

An alternative characterization of Gahler's definition of regularity of a lattice-valued convergence space is given. In particular, a space is regular exactly whenever convergence of filters remains invariant with respect to taking ''closures.'' Verification employs a slight modification of the work by Jager.

H. Boustique | Giles Richardson | H. Boustique | G. Richardson

[1] D. C. Kent,et al. Probablistic convergence spaces and regularity , 1997 .

[2] Horst Herrlich,et al. Recent developments of general topology and its applications : International Conference in Memory of Felix Hausdorff (1868-1942), Berlin, March 22-28, 1992 , 1992 .

[3] Gunther Jäger,et al. Compactification of lattice-valued convergence spaces , 2010, Fuzzy Sets Syst..

[4] Giles Richardson,et al. Lattice-valued convergence: Diagonal axioms , 2008, Fuzzy Sets Syst..

[5] Ulrich Höhle,et al. Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory , 1998 .

[6] Gunther Jäger,et al. Lattice-valued convergence spaces and regularity , 2008, Fuzzy Sets Syst..

[7] Alexander P. Sostak,et al. Axiomatic Foundations Of Fixed-Basis Fuzzy Topology , 1999 .

[8] Hans-Joachim Kowalsky,et al. Limesräume und Komplettierung , 1954 .

[9] C. H. Cook,et al. Regular convergence spaces , 1967 .

[10] Hans-Joachim Kowalsky,et al. Beiträge zur topologischen Algebra , 1954 .