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Two notes on nuclei. (English) Zbl 0722.06007
This paper presents explicit formulae for the nucleus generated by a prenucleus on a frame, and for the fibrewise closure of a nucleus on a frame. An example is given to show that the ‘simple-minded’ construction of the fibrewise closure yields only a prenucleus rather than a nucleus in general. These constructions were introduced as part of the author’s attempts to show that the fibrewise closed nuclei on a frame form a subframe of the frame of all nuclei, but in the event they turned out not to be needed for this purpose [cf. the author and M. Jibladze, The frame of fibrewise closed nuclei, Cah. Topologie Géom. Différ. Catégoriques (to appear)].
Reviewer: P.T.Johnstone

MSC:
06D99 Distributive lattices
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