Two notes on nuclei (Q2641324)

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 \textit{M. Jibladze}, The frame of fibrewise closed nuclei, Cah. Topologie Géom. Différ. Catégoriques (to appear)].