Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 3, Issue 1, April 2019, Pages: 41-46

One-point Ultra-F Compactification and Stone-Cech Ultra-F compactification of L-topological Spaces

Hanchuan LU 1,2* and Wenqing FU2

1School of Mathematical Sciences, Nanjing Normal University, Nanjing, P.R. China
2School of Mathematics and Statistics, Guizhou University, Guiyang, P.R. China
3School of Science, Xi’an Technological University, Xi’an, P.R. China


In this paper, a method of getting Ultra-F compactification and Stone-Cech Ultra-F compactification of L-topology is given. We give the necessary and sufficient conditions of Stone-Cech Ultra-F compactification of Ltopological spaces, and prove that it is unique in the sense of homeomorphism. Further, it is proved that an L−topology space is locally Ultra-F compact and Hausdorff if and only if its one-point compactificated space is Ultra-F compact and Hausdorff.


L-topology, Stone-Cech compactification, Ultra-F compactification, one-point Ultra-F Compactification


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1. Zadeh LA. Fuzzy sets. Inf Control 1965, 8: 338-353.

2. Chang CL. Fuzzy topological spaces. J Math Anal Appl 1968, 24:39-90.

3. Liu YM, Luo MK. Fuzzy topology. World Scientific, Singapore, 1997.

4. Wang GJ. Theory of L-fuzzy topological space. Shaanxi Normal University Press, Xi’an, 1988 (in Chinese).

5. Hol´a L’, Novotny B. Topology of uniform convergence and compactification. Journal of Mathematical Analysis and Applications 2015, 424 :470-474.

6. Wu HJ, Wu WH. A net and open-filter process of compactification and the Stone-Cech,Wallman compactifications. ˇ Topology and its Applications 2006, 153: 1291-1301.

7. Fox KM. Extending the class of known Stone-Cech remainders for -spaces. Topology and its Applications 2015, 190: 1-8.

8. Kelley JL. General Topology. Van Nostrand, Princeton, NJ, 1955.

9. Liu YM, Luo MK. Fuzzy Stone-Cech-type compactifications. Fuzzy Sets and Systems 1989; 3: 355-372.

10. Liu YM, Luo MK. Fuzzy Stone-Cech compactifications and the largest Tychonoff compactifications. A Chinese summary appears in Chinese Ann. Math. Ser. A 1989; 1: 106. Chinese Ann. Math. Ser. B 1989; 1: 74-84.

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