Geodesic
A new form of fuzzy $\alpha $-compactness
Mathematica Bohemica, Tome 131 (2006) no. 1, pp. 15-28
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A new form of $\alpha $-compactness is introduced in $L$-topological spaces by $\alpha $-open $L$-sets and their inequality where $L$ is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice $L$. It can also be characterized by means of $\alpha $-closed $L$-sets and their inequality. When $L$ is a completely distributive de Morgan algebra, its many characterizations are presented and the relations between it and the other types of compactness are discussed. Countable $\alpha $-compactness and the $\alpha $-Lindelöf property are also researched.
A new form of $\alpha $-compactness is introduced in $L$-topological spaces by $\alpha $-open $L$-sets and their inequality where $L$ is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice $L$. It can also be characterized by means of $\alpha $-closed $L$-sets and their inequality. When $L$ is a completely distributive de Morgan algebra, its many characterizations are presented and the relations between it and the other types of compactness are discussed. Countable $\alpha $-compactness and the $\alpha $-Lindelöf property are also researched.
DOI : 10.21136/MB.2006.134081
Classification : 54A40, 54D35
Keywords: $L$-topology; compactness; $\alpha $-compactness; countable $\alpha $-compactness; $\alpha $-Lindelöf property; $\alpha $-irresolute map; $\alpha $-continuous map 
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Shi, Fu-Gui. A new form of fuzzy $\alpha $-compactness. Mathematica Bohemica, Tome 131 (2006) no. 1, pp. 15-28. doi: 10.21136/MB.2006.134081

[1] H. Aygün: $\alpha $-compactness in $L$-fuzzy topological spaces. Fuzzy Sets Syst. 116 (2000), 317–324. | MR

[2] K. K. Azad: On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weak continuity. J. Math. Anal. Appl. 82 (1981), 14–32. | DOI | MR

[3] S. Z. Bai: Fuzzy strongly semiopen sets and fuzzy strong semicontinuity. Fuzzy Sets Syst. 52 (1992), 345–351. | MR | Zbl

[4] S. Z. Bai: The SR-compactness in $L$-fuzzy topological spaces. Fuzzy Sets Syst. 87 (1997), 219–225. | MR | Zbl

[5] P. Dwinger: Characterization of the complete homomorphic images of a completely distributive complete lattice. I. Indagationes Mathematicae (Proceedings) 85 (1982), 403–414. | DOI | MR | Zbl

[6] G. Gierz, et al.: A Compendium of Continuous Lattices. Springer, Berlin, 1980. | MR | Zbl

[7] S. R. T. Kudri: Compactness in $L$-fuzzy topological spaces. Fuzzy Sets Syst. 67 (1994), 329–336. | MR | Zbl

[8] S. G. Li, S. Z. Bai, N. Li: The near SR-compactness axiom in $L$-topological spaces. Fuzzy Sets Syst. 147 (2004), 307–316. | MR

[9] Y. M. Liu, M. K. Luo: Fuzzy Topology. World Scientific, Singapore, 1997. | MR

[10] R. Lowen: A comparison of different compactness notions in fuzzy topological spaces. J. Math. Anal. Appl. 64 (1978), 446–454. | DOI | MR | Zbl

[11] S. N. Maheshwari, S. S. Thakur: On $\alpha $-irresolute mappings. Tamkang J. Math. 11 (1981), 209–214. | MR

[12] S. N. Maheshwari, S. S. Thakur: On $\alpha $-compact spaces. Bull. Inst. Math. Acad. Sinica 13 (1985), 341–347. | MR

[13] O. Njåstad: On some classes of nearly open sets. Pacific J. Math. 15 (1965), 961–970. | DOI | MR

[14] A. S. B. Shahana: On fuzzy strong semicontinuity and fuzzy precontinuity. Fuzzy Sets Syst. 44 (1991), 303–308. | MR

[15] F.-G. Shi: Fuzzy compactness in $L$-topological spaces. Fuzzy Sets Syst., submitted. | Zbl

[16] F.-G. Shi: Countable compactness and the Lindelöf property of $L$-fuzzy sets. Iran. J. Fuzzy Syst. 1 (2004), 79–88. | MR | Zbl

[17] F.-G. Shi: Theory of $L_\beta $-nested sets and $L_\alpha $-nested and their applications. Fuzzy Systems and Mathematics 4 (1995), 65–72. (Chinese) | MR

[18] S. S. Thakur, R. K. Saraf: $\alpha $-compact fuzzy topological spaces. Math. Bohem. 120 (1995), 299–303. | MR

[19] G. J. Wang: Theory of $L$-fuzzy Topological Spaces. Shanxi Normal University Press, Xian, 1988. (Chinese)

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