Weak forms of continuity and openness
DOI:
https://doi.org/10.4067/S0716-09172016000300006Keywords:
Topological spaces, δ-preopen sets, δ-precontinuity, somewhat δ-precontinuity, espacios topológicos, conjunto δ-preabierto, precontinuidad-δ.Abstract
Some new class of functions, called somewhat δ-precontinuous, somewhat δ-preopen and hardly δ-preopen functions, have been defined and studied by utilizing δ-preopen sets. Moreover, characterizations and properties of these functions are presented.References
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[2] M.Caldas, T. Fukutake, S. Jafari and T. Noiri, An Alexandroff space defined by δ-preopen sets, Bull. Fukuoka Univ. Ed., 54, Part III, pp. 1-6, (2005).
[3] M. Caldas, S. Jafari T.Noiri and M.Simoes, More on contra-δ-precontinuous functions, Miskolc Math. Notes, 9, pp. 25-32, (2008).
[4] E. Ekici, (δ-pre,s)-continuous functions, Bull. Malaysian Math. Sci. Soc., 27(2), pp. 237-251, (2004).
[5] E. Ekici, On δp-connected spaces, Bull. Carpathian J. Math., in press.
[6] E. Ekici, δ-preopen sets, Mathematica, Tome 47(70), No. 2, pp. 157-164, (2005).
[7] K.R. Gently and H.B. Hoyle, Somewhat continuous functions, Czechslovak Math. J., 21, pp. 5-12, (1971).
[8] M. Ganster, Preopen sets and resolvable spaces, Kyungpook Math. J., 27 (2), pp. 135-143, (1987).
[9] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (2), pp. 89-96, (1970).
[10] S. Raychaudhuri, Concerning δ*-almost continuity and δ-preregularity, Bull. Calcutta Math. Soc., 85, pp. 385-392, (1993).
[11] S. Raychaudhuri and M. N. Mukherjee, On δ-almost continuity and δ-preopen sets, Bull. Inst. Math. Acad. Sinica, 21, pp. 357-366, (1993).
[12] S. Raychaudhuri and M. N. Mukherjee, δp-closedness for topological spaces, J. Indian Acad. Math., 18, pp. 89-99 (1996).
[13] N. V. Velicko, H-closed topological spaces, Mat. Sb., 70 (1966), 98-112; English transl., Amer. Math. Soc. Transl., 78, pp. 103-118, (1968).
Published
2017-03-23
How to Cite
[1]
M. Caldas Cueva and S. Jafari, “Weak forms of continuity and openness”, Proyecciones (Antofagasta, On line), vol. 35, no. 3, pp. 289-300, Mar. 2017.
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