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| FUZZY STONE-CECH COMPACTIFICATIONS AND THE LARGEST TYCHONOFF COMPACTIFICATIONS |
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Citation： |
Liu Yingming,Luo Maokang.FUZZY STONE-CECH COMPACTIFICATIONS AND THE LARGEST TYCHONOFF COMPACTIFICATIONS[J].Chinese Annals of Mathematics B,1989,10(1):74~84 |
| Page view： 881
Net amount： 752 |
Authors： |
Liu Yingming; Luo Maokang |
Foundation： |
Project Supported Partly by the National Science Fund of China. |
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| Abstract： |
Using the imbedding $theory^{[6]}$ and the N-compactness of L-fuzzy unit $interval^{[10]}$, the authors establish the Stone-Cech compactification theory of Tychonoff spaces. As well known, the Stone-Cech compactification in general topology is the largest compactification of all the Tychonoff compactifications. But this important property is not true in fuzzy
topology. The process of the argument of this negative result is very helpful for establishing a more reasonable Stone-Cech compactification theory^{[12]}$. Moreover, as relative results, the metrization theorem of induced spaces and the structure of quasi-Boolean lattice seem to have independent interest. |
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