R-Countability Axioms

• Authors: Amel Emhemed Kornas , Khadiga Ali Arwini
• Languages of publication: EN

Abstracts

EN

In this article, we use the concept of regular open sets to define a generalization of the countability axioms; namely regular countability axioms, and they are denoted by r-countability axioms. This class of axioms includes r-separable spaces, r-first countable spaces, r-Lindelöf spaces, r-𝜎-compact spaces and r-second countable spaces. We investigate their fundamental properties, and study the implication of the new axioms among themselves and with the known axioms. Moreover, we study the hereditary properties for r-countability axioms, also we consider some related functions in terms of r-open sets, which preserve these spaces. Finally, we prove that in regular space r-countability axioms and countability axioms are equivalent, while in locally compact T_2 space, the spaces: Lindelöf, r- Lindelöf, 𝜎-compact and r-𝜎-compact are all equivalent.

Keywords

EN

Countability axioms; Lindelöf spaces; compact spaces; regular open sets; 𝜎-compact spaces

Discipline

• INFORMATICS: INFORMATICS

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World Scientific News
• Year: 2020
• Volume: 149
• Pages: 92-109

Contributors

author

Amel Emhemed Kornas

• Mathematics Department, Higher Institute of Science and Technology, Tripoli, Libya

author

Khadiga Ali Arwini

• Mathematics Department, Tripoli University, Tripoli, Libya

References

• M. H. Stone. Applications of the Theory of Boolean Rings to General Topology. Trans. Am. Math. Soc. 41 (1937) 375-481
• C. Ronse. Regular Open or Closed Sets. Philips Research Laboratory Brussels, A v. E van Beclaere 2 B (1990) 1170
• H. K. Abdullah and F. K. Radhy. Strongly Regular Proper Mappings. Journal of Al-Qadisiyah for Computer Science and Mathematics 3(1) (2011) 185-204
• Charles Dorsett. New Characterizations of Regular Open Sets, Semi-Regular Sets and Extremely Disconnectedness. Math. Slovaca 45 (4) (1995) 435-444
• Charles Dorsett. Regularly Open Sets and R-Topological properties. Nat. Acod. Sci. Letters, 10 (1987) 17-21
• Hisham Mahdi, Fadwa Nasser. On Minimal and Maximal Regular Open Sets. Mathematics and Statistics 5 (2) (2017) 78-83
• N. Levine. Generalized Closed Sets in Topology. Rend. Circ. Mat. Palermo 19(12) (1970) 1170
• J. Dontchev and M. Ganster. On Minimal Door, Minimal Anti Compact and Minimal T_□(3/4)-Spaces. Mathematical Proceedings of the Royal Irish Academy 98A (2) (1998) 209-215.
• S. Balasubramanian. Generalized Separation Axioms. Saentia Magna 6 (4) (2010) 1-4
• M. K. Singhal and A. Mathur. On Nearly Compact spaces. Boll. U.M.L. 4 (6) (1969) 10-702
• A. S. Mashhour, I. A. Hasanein and M. E. Abd El-Monsef. Remarks on Nearly Compact Spaces. Indian J. Pure Appl. Math. 12 (6) (1981) 685-690
• R. A. H. Al-Abdulla and F. A. Shneef. On Coc-r-Compact Spaces, Journal of Al-Qadisiyah for Computer Science and Mathematics 9 (1) (2017) 1-11
• G. Balasubramanian. On Some Generalizations of Compact Spaces. Glasnik Mathematics 17 (37) (1982) 367-380
• F. Cammaroto and G. Santoro. Some Counterexamples and Properties on Generalizations of Lindelöf Spaces. International Journal of Mathematics and Mathematics Sciences 19 (4) (1996) 737-746
• A. J. Fawakhreh and A. Kilicman. Mappings and Some Decompositions of Continuity on Nearly Lindelöf Spaces. Akademiai Kiado, Budapest 97 (3) (2002) 199-206.
• D. Jankovic and Ch. Konstadilaki. On Covering Properties by Regular Closed Sets. Math. Pannonica. 7 (1996) 97-111
• M. S. Sarsak. More on RC-Lindelöf Sets and Almost RC-Lindelöf Sets. International Journal of Mathematics and Mathematical Sciences 20 (2006) 1-9
• S. Willard. General Topology, Addison-Wesley Publishing Company, United States of American (1970).
• John. L. Kelley. General Topology, Graduate Text in Mathematics, Springer (1975).
• K. A. Arwini and A. E. Kornas. D-Countability Axioms. An International Scientific Journal 143 (2020) 28-38

• Document Type: article