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On lattice-valued frames: The completely distributive case
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DOI：10.1016/j.fss.2009.10.024.png)
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Abstract
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We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames parts I and II, FUZZY Sets and Systems 159 (2008) 501-528 and 529-558] by relaxing the assumption that L be a complete chain As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a completely distributive lattice. In particular, L-Frm is complete and cocomplete Finally we prove that, in a certain sense. the assumption of L being a completely distributive lattice cannot be weakened (C) 2009 Elsevier B.V. All rights reserved
Keywords:
L-frames
L-Frm
Completely distributive lattice
L-topological space
L-Top
Iota functor
Completeness
Cocompleteness
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