PL EN


Preferences help
enabled [disable] Abstract
Number of results
2020 | 144 | 158-168
Article title

Separation Axioms Weaker Than T1

Content
Title variants
Languages of publication
EN
Abstracts
EN
The purpose of this paper is to introduce a new type of separation axioms via dense sets, called DT_i-spaces (i = 0‚1/( 4) ‚1/( 3) ‚1/( 2)‚3/( 4)‚1), where a DT_i-space is a topological space which contains a dense T_i-subspace (i = 0‚1/( 4) ‚1/( 3) ‚ 1/( 2) ‚3/( 4)‚1). These new axioms are weaker than the axiom of T_□1. We provide the basic properties of DT_i- spaces (i = 0‚1/( 4)‚1/( 3) ‚1/( 2) ‚3/( 4)‚1), and we show that the axioms of DT_□((1 )/4), DT_□(1/3),〖 DT〗_□(1/2), DT_□(3/4), DT_□1 are open hereditary. Moreover, we study the connections between these axioms and the axioms of T_i where (i = 0‚1/( 4) ‚1/( 3) ‚1/( 2) ‚3/( 4)‚1).
Year
Volume
144
Pages
158-168
Physical description
Contributors
  • Department of Mathematics, Tripoli University, Tripoli, Libya
  • Department of Mathematics, Higher Institute of Science and Technology, Tripoli, Libya
References
  • M. Caldas‚ S. Jafari and G. Navalagi. More on λ-closed sets in topological spaces. Revista Columbiana de Mathematical 41 (2) (2007) 355-369
  • K. Kannan. On Levine’s Generalized closed sets. A survey, Research Journal of Applied Sciences, Engineering and Technology 4 (11) (2012) 1612-1615
  • C. Ronse. Regular open or closed sets. Philips Research Laboratory Brussels, A v. E van Becelaere 2 B (1990) 1170
  • M. P. Chaudhary, Vinesh Kumar. On g-closed sets in a topological space. Global Journal of Science Frontier Research 10 (2) (2010) 10-12
  • Zanyar A. Ameen. On types of generalized closed sets. Journal of Taibah University for Science 12 (3) (2018) 290-293
  • N. Araki, M. Ganster, H. Maki and A. Nishi. Properties of T1/4 spaces. Questions and Answers in General Topology 24 (2) (2006) 143-148
  • Francisco G. Arenas, Julian Dontchev and Maximilian Ganster. On λ-sets and the dual of generalized continuity. Questions Answers in Gen Topology 15 (1) (1997) 3-13
  • F.G. Arenas, J. Dontchev and M.L. Puertas. Unification approach to the separation axioms between T_□0 and completely hausdorff. Acta Math. Hungar 86 (2000) 75-82
  • Francisco G. Arenas, Julian Dontchev and Maria Luz Puertas. Idealization of some weak separation axioms. Acta Mathematica Hungarica Source 89 (2000) 47-53
  • J. Dontchev and M. Ganster. On minimal door, minimal anti compact and minimal T_□(3/4)-spaces. Mathematical Proceedings of the Royal Irish Academy 98 A (2) (1998) 209-215
  • W. Dunham. T_□(1/2)-space. Kyungpook Math J (17) (1977) 161-169
  • N. Levine. Generalized closed sets in topology. Rend. Circ. Mat. Palermo 19 (2) (1970) 89-96
  • H. Maki‚ J. Umehara and K.Yamamura. Characterizations of T_□(1/2)-spaces using generalized V-sets. Indian J. Pure Appl. Math 19 (7) (1988) 634-640
  • Miguel Caldas, Saeid Jafari, Govindappa Navalagi. More on λ-closed sets in topological spaces. Revista Colombiana de Matematicas 41 (2) (2007) 355-369
  • M. S. Sarsak. New separation axioms in generalized topological spaces. Acta Math. Hungar 132 (3) (2011) 244-252
  • Chandan Chattopadhyay. Some new separation axioms a different approach. Global Journal of Mathematical Sciences: Theory and Practical 3 (3) (2011) 289-297
  • Adea Khaleafa Hussain, Ali Saadi Abd Alatif. Characterizations and properties of b-T_(□(1/( 2))) spaces. Iraqi Journal of Science 53 (4) (2012) 861-865
  • Raghu Gompa, Vijaya L. Gompa. Local separation axioms between Kolmogorov and Frechet spaces. Missouri J. Math. Sci 29 (1) (2017) 33-42
  • S. Willard, General Topology. Addison-Wesley Publishing Company, United States of American (1970).
  • T. Shyla isac mary and P. Thangavelu. On Regular Pre-Semiclosed Sets in Topological Spaces. KBM Journal of Mathematical sciences and Computer Applications 1(1) (2010) 9-17
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-a6a92fa6-6ea7-4bd8-8693-f0b1796ed783
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.