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Extending semilattices to frames using sites and coverages

In: Mathematica Slovaca, vol. 64, no. 3
Richard N. Ball - Aleš Pultr
Detaily:
Rok, strany: 2014, 527 - 544
Kľúčové slová:
site, coverage, frame, meet semilattice, joins in meet semilattices
O článku:
Each meet semilattice $S$ is well known to be freely extended to a frame by its down-sets $\mathfrak{D}S$. In this article we present, first, the complete range of frame extensions generated by $S$; it turns out to be a sub-coframe of the coframe $C$ of sublocales of $\mathfrak{D}S$, indeed, an interval in $C$, with \mathfrak{D}S$ as the top and the extension of $S$ respecting all the exact joins in $S$ as the bottom. Then, the Heyting and Boolean case is discussed; there, the bottom extension is shown to coincide with the Dedekind-MacNeille completion. The technique used is a technique of sites, generalizing that used in [JOHNSTONE, P. T.: Stone Spaces. Cambridge Stud. Adv. Math. 3, Cambridge University Press, Cambridge, 1982].
Ako citovať:
ISO 690:
Ball, R., Pultr, A. 2014. Extending semilattices to frames using sites and coverages. In Mathematica Slovaca, vol. 64, no.3, pp. 527-544. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0223-9

APA:
Ball, R., Pultr, A. (2014). Extending semilattices to frames using sites and coverages. Mathematica Slovaca, 64(3), 527-544. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0223-9
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