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A note on topological $$D$$-posets of fuzzy sets. (English) Zbl 0922.06001
Summary: F. Kôpka and F. Chovanec [Math. Slovaka 44, 21-34 (1994; Zbl 0789.03048)] defined a 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 also prove some consequences for the continuity of the difference operation on $$D$$-posets of fuzzy sets.
##### MSC:
 06A06 Partial orders, general 26E50 Fuzzy real analysis 03G12 Quantum logic
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