Journal
FUZZY SETS AND SYSTEMS
Volume 420, Issue -, Pages 143-156Publisher
ELSEVIER
DOI: 10.1016/j.fss.2021.02.004
Keywords
Topology; Category; L-topology; Open filter monad; Eilenberg-Moore algebra; L-Scott topology; L-continuous lattice
Funding
- National Natural Science Foundation of China [11871189, 11971448]
- Natural Science Foundation of Hebei Province [A2020208008]
- Startup Foundation for Introducing Talent of NUIST [2019r63]
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The paper demonstrates that the collections of open filters of T-0 L-topological spaces form a monad, and concludes that the Eilenberg-Moore algebras of the open filter monad are precisely L-continuous lattices. Additionally, it shows that the category of L-continuous lattices is strictly monadic over the category of T-0 L-topological spaces.
With a frame L as the truth value table, we prove that the collections of open filters of T-0 L-topological spaces form a monad. By means of L-Scott topology and the specialization L-order, we get the main results: (1) the Eilenberg-Moore algebras of the open filter monad are precisely L-continuous lattices; (2) the category of L-continuous lattices is strictly monadic over the category of T-0 L-topological spaces. (C) 2021 Elsevier B.V. All rights reserved.
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