ARE HIGHER FUZZY SEPARATION AXIOMS GOOD EXTENSIONS?

Abstract

A system of separation axioms for fuzzy topological spaces has been introduced by Hutton and Reilly [Fuzzy Sets Syst. 3 (1980), 93–104]. Wang and Hu [J. Math. Anal. Appl. 108 (1985), 495–5061 proved that the lower ones are good extensions in the sense of Lowen [J. Math. Anal. Appl. 64 (1978), 446–4541. We close this gap by proving that also the higher separation axioms are good extensions of the corresponding topological axioms.