Abstract
This chapter introduces lattice-valued frames or L- frames, related to traditional frames analogously to how L-topological spaces relate to traditional spaces, via level sets and level mappings viewed as systems of frame morphisms (Proposition 3.3.2). En route, the well-known S2 and LS2 functors [25, 10, 11, 12, 16, 17, 18, 29, 33, 43, 44, 48, 54, 55, 56, 57, 58, 61] relating traditional spaces and L-spaces, respectively, to their associated (semi)locales of open and L-open sets are analogized and modified. This study both gives new descriptions of classes of sober spaces extant in the literature and creates a new class of sober spaces, justifying examples for which are given in Chapter 17 [42] of this Volume.
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Pultr, A., Rodabaugh, S.E. (2003). Lattice-Valued Frames, Functor Categories, And Classes Of Sober Spaces. In: Rodabaugh, S.E., Klement, E.P. (eds) Topological and Algebraic Structures in Fuzzy Sets. Trends in Logic, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0231-7_7
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DOI: https://doi.org/10.1007/978-94-017-0231-7_7
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