Upper and Lower θp-Continuous Multifunctions

Abstract

We introduce two new types of multifunctions, namely upper (lower) $\theta $p$-$continuous multifunctions, between topological spaces. Besides characterising these multifunctions, we study some properties of upper $\theta $p$-$continuous multifunctions.

Keywords

• Pre-$\theta $-open sets
• strongly $\theta $-precontinuity
• multifunction

References

1. Banzaru, T., Multifunctions and M-product spaces, Bull. Stiin. Teh. Inst. Politeh Timisoara Ser. Mat. Fiz Mer. Teor. Apl., 17(1972), 17–23.
2. Berge, C., Espaces TopologiquesFfonctions Multivoques, Dunod, Paris, 1959.
3. Cho, S.H., A note on strongly θ-precontinuous functions, Acta Math. Hungar., 101(2003), 173–178.
4. Dontchev, J., Ganster M., Noiri, T., On p-closed spaces, Internat. J. Math. Math. Sci., 24(2002), 203–212.
5. El-Deeb, N., Hasanein, I.A., Mashhour, A.S., Noiri, T., On p-regular spaces, Bull. Math. Soc. Sci. Math. R.S. Roumanie, 27(75)(1983), 311–315.
6. Mashhour, A.S., Abd El-Monsef M.E., El-Deeb, S.N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Egypt, 53(1982), 47–53.
7. Mashhour, A.S., Hasanein, I.A., El-Deeb, S.N., A note on semi-continuity and precontinuity, Indian J. Pure Appl. Math., 13(1982), 1119–1123.
8. Mukherjee, M.N., Raychaudhuri, S., Sinha, P., On upper and lower θ∗-continuous multifunctions, Southeast Asian Bulletin of Mathematics, 26(2002), 841–855.

9. Njastad, O., On some classes of nearly open sets, Pacific J. Math., 15(1965), 961–970.
10. Noiri, T., Strongly θ-precontinuous functions, Acta Math. Hungar., 90(2001), 307–316.
11. Nour, T.M.J., Contributions to the Theory of Bitopological Spaces, Ph.D. Thesis, Univ. of Delhi, 1989.
12. Popa, V., Some properties of H-almost continuous multifunctions, Probl. Math., 10(1988), 9–26.
13. Velicko, N.V., H-closed topological spaces, Amer. Math. Soc. Transl., 78(1968), 103–118.
14. Whyburn, G.T., Retracting multifunctions, Proc. Nat. Acad. Sci. U.S.A., 59(1968), 343–348.