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- W45549531 abstract "In this paper we investigate the fuzzy sets with lattice (precisely, fuzzy lattice) values. Some new global properties on the weakly induced spaces and induced spaces are obtained. Based on these results, we take the induced space of real unit interval I as new basic space and establish a reasonable theory of Stone-Čech compactifications via fuzzy imbedding theory [5] and N-compactness [10, 12]. For so-called T312∗ and weakly induced spaces, its Stone-Čech-type compactification always exists. We give a counterexample to show that the previous Stone-Čech compactification [6] is not the largest T2 compactification of a given space. Compared with this, we now have a positive results for the new Stone-Čech-type compactification. Moreover, although the preorder among the compactifications for a given space does not generally satisfy the anti-symmetric law, we fortunately establish uniqueness of the largest T2-type compactification among the compactifications for a given space." @default.
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- W45549531 date "1989-12-01" @default.
- W45549531 modified "2023-10-16" @default.
- W45549531 title "Fuzzy stone-Čech-type compactifications" @default.
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- W45549531 doi "https://doi.org/10.1016/0165-0114(89)90124-3" @default.
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