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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

06D99 Distributive lattices
Full Text: DOI
[1] J. S. Golan and H. Simmons (1988) Derivatives, Nuclei and Dimensions on the Frame of Torsion Theories, Pitman Research Notes in Math. no. 188, Longman/J. Wiley. · Zbl 0661.16020
[2] P. T. Johnstone (1982) Stone Spaces, Cambridge Studies in Advanced Math. no. 3, Cambridge University Press.
[3] P. T.Johnstone (1989) A constructive ?closed subgroup theorem? for localic groups and groupoids, Cahiers Top. Géom. Diff. Catégoriques 30, 3-23. · Zbl 0668.03028
[4] H.Simmons (1978) A framework for topology, in Logic Colloquium 77, Studies in Logic and the Foundations of Math. vol. 96, North-Holland, Amsterdam, pp. 239-251. · Zbl 0493.06005
[5] H.Simmons (1982) An algebraic version of Cantor-Bendixson analysis, in Categorical Aspects of Topology and Analysis, Lecture Notes in Math. vol. 915, Springer-Verlag, Berlin, pp. 310-323.
[6] D.Wigner (1979) Two notes on frames, J. Austral. Math. Soc. A 28, 257-268. · Zbl 0428.06004
[7] G. C. Wraith, personal communication, January 1989.
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