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2021 | 152 | 55-68

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Generalizations of Regular Closed Set


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In this article, we introduce several types of generalized regular closed sets in topological spaces, using the concepts of v-sets, the class of generalizations contains the sets; regular v-sets, generalized regular v-sets, generalized star v-set and generalized star regular ᴠ-set. We illustrate the inter-relations between these sets, then we study the characterization of this class, which relative to unions, intersections and subspaces, finally we investigate their behavior in regular spaces and extremely disconnected spaces.






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


  • H. Maki, Generalized. ᴧ -Sets And The Associated Closure Operator. The Special Issue in Commemoration of Prof. Kazusada IKEDA’s Retirement, 1 (1986) 139-146
  • H. Maki, J. Umehara and K. Yamamura, Characterizations Of T_(1/2)-Spaces Using Generalized v- Sets. Indian J. Pure Appl. Math 9 (7) (1988) 634-640
  • N. Levine, Generalized Closed Sets In Topology. Rend. Circ. Mat. Palermo, 19 (2) (1970) 89-96
  • W. Dunham, A New Closure Operator For Non T_1-Toplogies. Kyungpook Math. J, 22 (1982) 55-60
  • M. Caldas‚ S. Jafari and G. Navalagi‚ More On λ-Closed Sets In Topological Spaces. Revista Columbiana de Mathematical‚41 (2) (2007) 355-369
  • 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 And Closed Sets. Philips Research Laboratory Brissels, Ar. E Van Baclaera, 2 B (1990) 1170
  • Charles Dorsett, Regularly Open Sets And R-Topological Properties. Nat. Acod. Sci-Letters, 10 (1987) 17-21
  • H. K. Abdullah and F. K. Radhy, Strongly Regular Proper Mappings. Journal of Al-Qadisiyah for Computer Science and Mathematics 3 (1) (2011)
  • Zanyar A. Ameen, Baravan A. Asaad and Ramadhan A. Muhammed, On Super Classes Of -Open Sets In Topological Spaces. International Journal of Applied Mathematics, 32 (2) (2019) 259-277
  • A. E. Kornas and K. A. Arwini, R-Countability Axioms. An International Scientific Journal 149 (2020) 92-109
  • S. Willard, General Topology. Addison-Wesley Publishing Company, United States of American (1970).
  • Dona Papert Strauss, Extremally Disconnected Spaces. Proc. Amer. Math. Soc. 18 (1967) 305-309
  • Majid Mirmiran, A Note On Extremally Disconnected Spaces. Research Open Journal Of Information Science, 1 (1) (2013) 01-03
  • M. Caldas and J. Dontchev, G.ᴧ_s-Sets And G.v_s-Sets. Mem. Fac. Sci. Kochi Univ. Math. 21 (2000) 21-30
  • M. Caldas, D. N. Georgiou and S. Jafari, Study Of (ᴧ, α)-Closed Sets And Related Notions In Topoloical Spaces. Bull. Malays. Math. Sci. Soc 30 (2007) 23-36
  • M. Caldas, S. Jafari and T. Noiri, On ᴧ_b-Sets And The Associated Topology τᴧ_b. Acta Math. Hungar, 110 (2006) 337-345
  • M. Caldas and S. Jafari, Generalized ᴧ_δ-Sets And Related Topics. Georgian Math. J. 16 (2009) 247-256
  • F. Cammaroto and T. Noiri, On ᴧ_m-Sets And Related Topological Spaces. Acta Math. Hungar, 109 (2005) 261-279
  • M. Ganster, S. Jafari and T. Noiri, On Pre- ᴧ -Sets And Pre-v –Sets. Acta Math. Hungar, 95 (2002) 337-343
  • E. Hatir and T. Noiri, ᴧ_sp-Sets And Some Weak Separation Axioms. Acta Math. Hungar, 103 (2004) 225-232

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