Geodesic
$\alpha$-continuous and $\alpha$-irresolute multifunctions
Mathematica Bohemica, Tome 121 (1996) no. 4, pp. 415-424
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Recently Popa and Noiri [10] established some new characterizations and basic properties of $\alpha$-continuous multifunctions. In this paper, we improve some of their results and examine further properties of $\alpha$-continuous and $\alpha$-irresolute multifunctions. We also make corrections to some theorems of Neubrunn [7].
Recently Popa and Noiri [10] established some new characterizations and basic properties of $\alpha$-continuous multifunctions. In this paper, we improve some of their results and examine further properties of $\alpha$-continuous and $\alpha$-irresolute multifunctions. We also make corrections to some theorems of Neubrunn [7].
DOI : 10.21136/MB.1996.126038
Classification : 54C60, 54E55
Keywords: upper (lower) $\alpha$-continuous; upper (lower) $\alpha$-irresolute; strongly $\alpha$-closed graph; almost compact; almost paracompact 
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Cao, Jiling; Reilly, Ivan L. $\alpha$-continuous and $\alpha$-irresolute multifunctions. Mathematica Bohemica, Tome 121 (1996) no. 4, pp. 415-424. doi: 10.21136/MB.1996.126038

[1] C. E. Aull: Paгacompact subsets. General Topology and its Relations to Modern Analysis and Algebra II. Proc. of the Symposium Prague, 1966, Academia, Praha, 1967, pp. 45-51. | MR

[2] C. Berge: Topological spaces. Oliver and Boyd Ltd., 1963. | Zbl

[3] E. Klein A. Thompson: Theory of correspondences. A Wiley-Interscience Publication. John Wiley and Sons, 1984. | MR

[4] S. N. Maheshwari S. S. Thakur: On $\alpha$-irresolute functions. Tamkang J. Math. 11 (1980), 209-214. | MR

[5] S. N. Maheshwari S. S. Thakur: On $\alpha$-compact spaces. Bull. Inst. Math. Acad. Sinica 13 (1985), 341-347. | MR

[6] A. S. Mashhour I. A. Hasanein S. N. El-Deeb: $\alpha$-Continious and $\alpha$-open mappings. Acta Math. Hung. 41 (1983), 213-218. | DOI | MR

[7] T. Neubrunn: Strongly quasi-continuous multivalued mappings. General Topology and its Relations to Modern Analysis and Algebra VI. Proc. of the Symposium, Prague, 1986, Heldermann Verlag Berlin, 1988, pp. 351-359. | MR

[8] O. Njåstad: On some classes of nearly open sets. Pacific J. Math. 15 (1965), 961-970. | DOI | MR

[9] T. Noiri: On $\alpha$-continuous functions. Časopis Pěst. Mat. 109 (1984), 118-126. | MR | Zbl

[10] V. Popa T. Noiri: On upper and lower $\alpha$-continuous multifunctions. Math. Slovaca 4З (1993), 261-265. | MR

[11] I. L. Reilly M. K. Vamanamurthy: Connectedness and strong semi-continuity. Časopis Pěst. Mat. 109 (1984), 261-265. | MR

[12] I. L. Reilly M. K. Vamanamurthy: On $\alpha$-continuity in topological spaces. Acta Math. Hung. 45 (1985), 27-32. | DOI | MR

[13] I. L. Reilly M. K. Vamanamurthy: On $\alpha$-sets in topological spaces. Tamkang J. Math. 16 (1985), 7-11. | MR

[14] M. K. Singal R. Asha: On almost M-compact spaces. Ann. Soc. Sci. Bruxelles 82 (1968), 233-242. | MR | Zbl

[15] M. K. Singal S. P. Arya: On M-paracompact spaces. Math. Anal. 181 (1969), 119-133. | DOI | MR

[16] G. T. Whyburn: Retracting multifunctions. Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 343-348. | DOI | MR

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