A subset K of a lattice is said to be directed if for any a, b∊K there is c∊K with c ≥ a, b. A complete lattice L is called upper continuous if for every directed subset (aα) and every element b. The following is a slight improvement of [4; Anmerkung 1. 11, p. 11].
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Yuzo Utumi (1961) studied this question.
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