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 IJMNTA  Vol.6 No.3 , September 2017
On Decomposition of New Kinds of Continuity in Bitopological Space
Abstract: In many papers, new classes of sets had been studied in topological space, then the notion of continuity between any two topological spaces (a function from X to Y is continuous if the inverse image of each open set of Y is open in X) is studied via this new classes of sets. Here the authors also introduce new classes of sets called pj-b-preopen, pj-b-B set, pj-b-t set, pj-b-semi-open and pj-sb-generalized closed set in bitopological space [1] which is a set with two topologies defined on it, then they study the notion of continuity via this set and introduce some of the theories which are studying the decomposition of continuity via this set in bitopological space.
Cite this paper: Al-Malki, H. and Al-Blowi, S. (2017) On Decomposition of New Kinds of Continuity in Bitopological Space. International Journal of Modern Nonlinear Theory and Application, 6, 98-103. doi: 10.4236/ijmnta.2017.63009.
References

[1]   Kelly, J.C. (1963) Bitopological Space. Proceedings of the London Mathematical Society, 13, 71-89.
https://doi.org/10.1112/plms/s3-13.1.71

[2]   Andrijevic, D. (1996) On B-Open Sets. Matematichki Vesnik, 48, 59-64.

[3]   Andrijevic, D. (1986) Semi-Preopen Sets. Matematichki Vesnik, 38, 24-32.

[4]   Levine, N. (1861) A Decomposition of Continuity in Topological Spaces. American Mathematical Monthly, 68, 44-46.
https://doi.org/10.2307/2311363

[5]   Njastad, O. (1965) On Some Classes of Nearly Open Sets. Pacific Journal of Mathematics, 15, 961-970.
https://doi.org/10.2140/pjm.1965.15.961

[6]   Tong, J. (1989) On Decomposition of Continuity in Topological Spaces. Acta Mathematica Hungarica, 54, 51-55.
https://doi.org/10.1007/BF01950708

[7]   Al-Omari, A. and Noorani, M. (2008) Decomposition of Continuity via B-Open Set. Boletim da Sociedade Paranaense de Matematica, 26, 53-64.
https://doi.org/10.5269/bspm.v26i1-2.7402

[8]   Przemski, M.A. (1993) Decomposition of Continuity and α-Continuity. Acta Mathematica Hungarica, 61, 93-98.
https://doi.org/10.1007/BF01872101

[9]   Jelic, M. (1990) A Decomposition of Pairwise Continuity. J. Inst. Math. Comput. Sci. Math. Ser., 3, 25-29.

[10]   Al-Blowi, S.A. (2017) Decomposition of P-Continuity via PG-B-Open Set, PG-Locally B-Closed and PJ-D (c, b)-Set.

[11]   Khedr, F.H. and Al-Blowi, S.A. (2007) PJ-Γ Sets and PJ-Γ-Continuity in Bitobological Space (I). Journal of Mathematics and Computer Science, 36, 1-19.

[12]   Khedr, F.H. and Al-Blowi, S.A. (2007) PJ-Γ Sets and PJ-Γ-Continuity in Bitobological Space (II). Journal of Mathematics and Computer Science, 36, 21-41.

[13]   Arya, S.R. and Gupta, R. (1974) On Strongly Continuous Mappings. Kyungpook Mathematical Journal, 14, 131-143.

 
 
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