Weak forms of continuity and openness

Miguel Caldas Cueva, Saeid Jafari


Some new class of functions, called somewhat -precontinuous, somewhat -preopen and hardly -preopen functions, have been defined and studied by utilizing -preopen sets. Moreover, characterizations and properties of these functions are presented.

Palabras clave

Topological spaces; δ-preopen sets; δ-precontinuity; somewhat δ-precontinuity; espacios topológicos; conjunto δ-preabierto; precontinuidad-δ.

Texto completo:



M.Caldas, T. Fukutake, S. Jafari and T. Noiri, Some applications of δ-preopen sets in topological spaces, Bull. Inst. Math. Acad. Sinica, 33(3), pp. 361-276, (2005).

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).

M. Caldas, S. Jafari T.Noiri and M.Simoes, More on contra-δ-precontinuous functions, Miskolc Math. Notes, 9, pp. 25-32, (2008).

E. Ekici, (δ-pre,s)-continuous functions, Bull. Malaysian Math. Sci. Soc., 27(2), pp. 237-251, (2004).

E. Ekici, On δp-connected spaces, Bull. Carpathian J. Math., in press.

E. Ekici, δ-preopen sets, Mathematica, Tome 47(70), No. 2, pp. 157-164, (2005).

K.R. Gently and H.B. Hoyle, Somewhat continuous functions, Czechslovak Math. J., 21, pp. 5-12, (1971).

M. Ganster, Preopen sets and resolvable spaces, Kyungpook Math. J., 27 (2), pp. 135-143, (1987).

N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19 (2), pp. 89-96, (1970).

S. Raychaudhuri, Concerning δ∗-almost continuity and δ-preregularity, Bull. Calcutta Math. Soc., 85, pp. 385-392, (1993).

S. Raychaudhuri and M. N. Mukherjee, On δ-almost continuity and δ-preopen sets, Bull. Inst. Math. Acad. Sinica, 21, pp. 357-366, (1993).

S. Raychaudhuri and M. N. Mukherjee, δp-closedness for topological spaces, J. Indian Acad. Math., 18, pp. 89-99 (1996).

N. V. Velicko, H-closed topological spaces, Mat. Sb., 70 (1966), 98-112; English transl., Amer. Math. Soc. Transl., 78, pp. 103-118, (1968).

DOI: http://dx.doi.org/10.4067/S0716-09172016000300006

Enlaces refback

  • No hay ningún enlace refback.