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Delineation of $Omega$ bitopological spaces

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In the present paper, we study and analyse a function on a bitopological space which enabled us to derive a new bitopology on a given bitopological space. We explore various characterizations of the derived bitopological space and investigate the propinquity between both the bitopologies. Also we de ne new separation axioms on the bitopological spaces and study how a separation axiom on one bitopo- logical space in uences the other.

Abstract

In the present paper, we study and analyse a function on a bitopological space which enabled us to derive a new bitopology on a given bitopological space. We explore various characterizations of the derived bitopological space and investigate the propinquity between both the bitopologies. Also we de ne new separation axioms on the bitopological spaces and study how a separation axiom on one bitopo- logical space in uences the other.

참고문헌 (10)

  1. C. H. Savopoulou, "On Dutta's Bitopological Paracompactness", Indian J. pure Appl. Math., 12(7), pp.799~803 (1981)
  2. C. Kuratowski, "Sur l'operation A de l'analysis situs", Fund. Math., 3, pp.182~199 (1922)
  3. I. E. Cooke, "On bitopological compactness", J. Lond. Math. Soc, 8, pp.518~522 (1965)
  4. I. L. Reilly, "On bitopological separation properties", Nanta Mathematica, 5, pp.14~25 (1971)
  5. J. C. Kelley, "Bitopological Space", Proc. Lond. Math. Soc, 13(3), pp.71~89 (1963)
  6. K. Al-Joubi, "the topology of open sets", Al- Monareh, 9(2), pp.169~179 (2003)
  7. M. G. Murdeshwar, "Semi Hausdorff Spaces", Canad. Math. Bull., 9, pp.353~356 (1966)
  8. M. K. Singal, "Some more separation axioms in bitopological spaces", Annales de la Societe Scientifique de Bruxelles, 84, pp.207~230 (1970)
  9. P. Agarwal, "Accretion of A New Bitopology", ~
  10. P. Fletcher, "The comparison of topologies", Duke Math. J., 36, pp.325~331 (1969)

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