Mappings and Finite Product of Pairwise Expandable Spaces

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Jamal Oudetallah, Iqbal M. Batiha

Abstract

In this work, we intend to study certain mappings in bitopological spaces such as pairwise perfect and pairwise countably perfect mappings that possess the property (E). Some properties of such mappings are provided which have helped us to obtain some finite product theorems concerning with pairwise expandable and almost pairwise expandable spaces. Two illustrative examples are given to demonstrate the effectiveness of some proposed results.

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References

  1. J.C. Kelly, Bitopological Spaces, Proc. London Math. Soc. s3-13 (1963), 71–89. https://doi.org/10.1112/plms/s3-13.1.71.
  2. J. Oudetallah, I.M. Batiha, On Almost Expandability in Bitopological Spaces, Int. J. Open Probl. Computer Sci. Math. 14 (2021), 43-48.
  3. J. Oudetallah, M.M. Rousan, I.M. Batiha, On D-Metacompactness in Topological Spaces, J. Appl. Math. Inform. 39 (2021), 919–926. https://doi.org/10.14317/JAMI.2021.919.
  4. A.A. Hnaif, A.A. Tamimi, A.M. Abdalla, I. Jebril, A Fault-Handling Method for the Hamiltonian Cycle in the Hypercube Topology, Computers Mater. Continua. 68 (2021), 505-519. https://doi.org/10.32604/cmc.2021.016123.
  5. P. Fletcher, H.B. Hoyle, III, C.W. Patty, The Comparison of Topologies, Duke Math. J. 36 (1969), 325-331. https://doi.org/10.1215/s0012-7094-69-03641-2.
  6. T. Birsan, Compacite dans les espaces bitopologiques, An. st. univ. Iasi, s.I.a. Mat. 15 (1969), 317-328.
  7. I.L. Reilly, Bitopological Local Compactness, Indagationes Math. (Proc.) 75 (1972), 407–411. https://doi.org/10.1016/1385-7258(72)90037-6.
  8. M.C. Datta, Projective Bitopological Spaces, J. Aust. Math. Soc. 13 (1972), 327–334. https://doi.org/10.1017/s1446788700013744.
  9. H. Hdeib, A. Fora, On Pairwise Paracompact Spaces, Dirasat, IX(2) (1982), 21-29.
  10. A. Mukherjee, A.R. Choudhury, M.K. Bose, On Bitopological Spaces, J. Mech. Continua Math. Sci. 3 (2008), 00003.
  11. A. Killiman, Z. Salleh, Product Properties for Pairwise Lindelöf Spaces, Bull. Malays. Math. Sci. Soc. 34 (2011), 231-246.
  12. F. A. Abushaheen and H. Hdeib, On [a, b]-Compactness in Bitopological Spaces, Int. J. Pure Appl. Math. 110 (2016), 519-535. https://doi.org/10.12732/ijpam.v110i3.11.
  13. H. Qoqazeh, H. Hdeib, E.A. Osba, on Metacompactness in Bitopological Spaces, Int. J. Pure Appl. Math. 119 (2018), 191-206.
  14. J. Oudetallah, On Feebly Pairwise Expandable Space, J. Math. Comput. Sci. 11 (2021), 6216-6225. https://doi.org/10.28919/jmcs/6294.
  15. R. Engleking, General Topology, Heldermann Verlag, Berlin, 1989.