ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 64,   1   (1995)
pp.   43-46

A NOTE ON TOPOLOGICAL $D$-POSETS OF FUZZY SETS
V. PALKO

Abstract.  K\^opka and Chovanec in Ref. KCH defined the difference poset ($D$-poset) as a partially ordered set with a partial difference operation. We show in this paper that every difference operation on a dense subset of $\langle 0,1\rangle$ is continuous with respect to the usual topology of the real line. We prove also some consequences for the continuity of the difference operation on $D$-posets of fuzzy sets.

AMS subject classification.  06A06, 26E50
Keywords.  Difference poset, fuzzy sets