SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 1

A general framework for compactness in L-topological spaces

A. GHAREEB
Pages
67–75
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The method used in this paper shows that these results are valid for any kind of open L-sets and thus we do not need to repeat it for each kind separately.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A general framework for the concepts of compactness, countable compactness, and the Lindel¨of property are introduced in L-topological spaces by means of several kinds of open L-sets and their inequalities when L is a complete DeMorgan algebra.
📊
Key Findings & Data:A general framework for the concepts of compactness, countable compactness, and the Lindel¨of property are introduced in L-topological spaces by means of several kinds of open L-sets and their inequalities when L is a complete DeMorgan algebra.
💡
Conclusion & Impact:The method used in this paper shows that these results are valid for any kind of open L-sets and thus we do not need to repeat it for each kind separately.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A general framework for the concepts of compactness, countable compactness, and the Lindel¨of property are introduced in L-topological spaces by means of several kinds of open L-sets and their inequalities when L is a complete DeMorgan algebra. The method used in this paper shows that these results are valid for any kind of open L-sets and thus we do not need to repeat it for each kind separately.

🔖

Cite This Article

GHAREEB, A. (2022). A general framework for compactness in L-topological spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 1, 67–75. https://ajindex.com/articles/530495

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. Andrijevic, D. On b-open sets, Mat. Vesnik 48, 59Û-64, 1996
  2. Azad, K. K. On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82, 14-32, 1981
  3. Balasubâsamanian, G. On fuzzy (3-compact spaces and fuzzy (3-extremally disconnected spaces, Kybernetika 33, 271-277, 1997
  4. Bin Shahna, A. S. On fuzzy strong semicontinuity and fuzzy precontinuity, Fuzzy Sets and Systems 44, 303-308, 1991
  5. Chadwick, J.J. A generalized form of compactness in fuzzy topological spaces, J. Math. Anal. Appl. 162, 92-110, 1991
  6. Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl. 24, 39-90, 1968
  7. Dwinger, P. Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings) 85, 403-414, 1982
  8. Gantner, T. E., and Steinlage, R. C. and Warren, R. H. Compactness in fuzzy topological spaces, J. Math. Anal. Appl. 62, 547-562, 1978
  9. Gierz, G. et al. A Compendium of Continuous Lattices (Springer Verlag, Berlin, 1980)
  10. Hanafy, I. M. (3S*-compactness in L-fuzzy topological spaces, J. Nonlinear Sci. Appl. 9, 27-37, 2009
  11. Hanafy, I. M. Fuzzy ~f-open sets agid fuzzy 7-continuity, J. Fuzzy Math. 7, 419-430, 1999
  12. Höhle, U. and Rodabaugh, S. E. S. E. Rodabaugh, Ed. Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory 3 (Kluwer Academic Publishers, Boston/Dordrecht/London, 1999)
  13. Li, Z. F. Compactness in fuzzy topological spaces, Chinese Kexue Tongbao 6, 321-323, 1983
  14. Liu, Y. M. and Luo, M.K. Fuzzy Topology (World Scientific, Singapore, 1997)
  15. Liu, Y. M. Compactness and Tychnoff theorem in fuzzy topological spaces, Acta Mathemat-ica Sinica 24, 260-268, 1981
  16. Lowen, R. A comparsion of different compactness notions in fuzzy topological spaces, J. Math. Anal. Appl. 64, 446-454, 1978
  17. Lowen, R. Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56, 621-633, 1976
  18. Rodabauglı, S. E. Point-set lattice-theoretic topology, Fuzzy Sets and Systems 40, 297-345, 1991
  19. Shi, F.-G. P-compactness in L-topological spaces, J. Nonlinear Sci. Appl. 2, 225-233, 2009
  20. Shi, F.-G. A new definition of fuzzy compactness, Fuzzy Sets and Systems 158, 1486-1495, 2007
  21. Shi, F.-G. A new form of fuzzy a-compactness, Mathematica Bohemica 131, 15-28, 2006
  22. Shi, F.-G. Semicompactness in L-topological spaces, International Journal of Mathematics and Mathematical Sciences 12, 1869-1878, 2