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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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