Weak forms of open mappings and α -topology

Duszyński, Zbigniew

doi:10.2478/v10127-009-0001-1

Abstract

The following notations associated with a mapping f : (X, τ) → (Y, σ) have been introduced in [D. S. Janković: A note on mappings of extremely disconnected spaces, Acta Math. Hungar. (1985), 83-92]: where for each x ∊ X. Interrelationships between well-known openness-type properties (a.o.S., w.o., -openness, a.o.W.) for f, f_*, f^α, f_α are studied.

References

[1] ARYA, S. P.-BHAMINI, M. P.: A generalization of normal spaces, Mat. Vesnik 35 (1983), 1-10.
Search in Google Scholar
[2] CROSSLEY, C. G.-HILDEBRAND, S. K.: Semi-closure, Texas J. Sci. 22 (1971), 99-112.
Search in Google Scholar
[3] CROSSLEY, C. G.-HILDEBRAND, S. K.: Semi-topological properties, Fund. Math. 74 (1972), 233-254.10.4064/fm-74-3-233-254
Search in Google Scholar
[4] DUSZYNSKI, Z.: Almost openness and, weak openness of mappings, submitted.
Search in Google Scholar
[5] GARG, G. L.-SIVARAJ, D.: Semitopological properties, Mat. Vesnik 36 (1984), 137-142.
Search in Google Scholar
[6] HUSAIN, Т.: Almost continuous mappings, Prace Mat. 10 (1966), 1-7.
Search in Google Scholar
[7] JANKOVIC, D. S.: A note on mappings of extremally disconnected spaces, Acta Math. Hungar. 46 (1985), 83-92.10.1007/BF01961010
Search in Google Scholar
[8] LEVINE, N.: Semi-open sets and, semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.10.1080/00029890.1963.11990039
Search in Google Scholar
[9] MASHHOUR, A. S.-ABD EL-MONSEF, M. E.-EL-DEEB, S. N.: On precontinuous and, weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.
Search in Google Scholar
[10] MASHHOUR, A. S.-HASANEIN, I. A.-EL-DEEB, S. N.: a-continuous and, a-open mappings, Acta Math. Hungar. 41 (1983), 213-218.10.1007/BF01961309
Search in Google Scholar
[11] NEUBRUNNOVA, A.: On certain generalizations of the notion of continuity, Mat. cas. 23 (1973), 374-380.
Search in Google Scholar
[12] NJASTAD, O.: On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.10.2140/pjm.1965.15.961
Search in Google Scholar
[13] NOIRI, Т.: On semi-continuous mappings, Atti Accad. Naz. Lincei, VIII. Ser., Rend., CI. Sci. Fis. Mat. Natur. 54 (1973), 210-214.
Search in Google Scholar
[14] NOIRI, Т.: A generalization of closed mappings, Atti Accad. Naz. Lincei, VIII. Ser., Rend., CI. Sci. Fis. Mat. Natur. 54 (1973), 412-415.
Search in Google Scholar
[15] NOIRI, Т.: Semi-continuity and, weak-continuity, Czechoslovak Math. J. 31 (106) (1981), 314-321.10.21136/CMJ.1981.101746
Search in Google Scholar
[16] NOIRI, Т.: Almost-open functions, Indian J. Math. 25 (1983), 73-79.
Search in Google Scholar
[17] NOIRI, Т.: On a-continuous functions, Cas. pest. mat. 109 (1984), 118-126.
Search in Google Scholar
[18] REILLY, I. L.-VAMANAMURTHY, M. K.: On a-continuity in topological spaces, Acta Math. Hungar. 45 (1985), 27-32.10.1007/BF01955019
Search in Google Scholar
[19] ROSE, D. A.: Weak openness and, almost openness, Internat. J. Math. Math. Sci. 7 (1984), 35-40.10.1155/S0161171284000041
Search in Google Scholar
[20] ROSE, D. A.: Weak continuity and, almost continuity, Internat. J. Math. Math. Sci. 7 (1984), 311-318.10.1155/S0161171284000338
Search in Google Scholar
[21] SINGAL, M. K.- SINGAL, A. R.: Almost-continuous mappings, Yokohama Math. J. 16 (1968), 63-73.
Search in Google Scholar
[22] SIVARAJ, D.: A note on S-closed, spaces, Acta Math. Hungar. 44 (1984), 207-213.10.1007/BF01950272
Search in Google Scholar
[23] WILANSKY, A.: Topics in Functional Analysis, Lecture Notes in Math., Vol. 45, Springer- -Verlag, Berlin, 1967.10.1007/BFb0079844
Search in Google Scholar

Weak forms of open mappings and α -topology

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