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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.3 Antofagasta Sept. 2016

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

 

Weak forms of continuity and openness

 

Miguel Caldas

Universidade Federal Fluminense, Brasil 

Saeid Jafari 

College of Vestsjaelland South, Denmark


ABSTRACT

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.

2000 Mathematics Subject Classification : 54A40.

Key words and phrases : Topological spaces, -preopen sets, -precontinuity, somewhat -precontinuity.


REFERENCES

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

[2]    M.Caldas, T. Fukutake, S. Jafari and T. Noiri, An Alexandroff space defined by -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--precontinuous functions, Miskolc Math. Notes, 9, pp. 25-32, (2008).

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

[5]    E. Ekici, On p-connected spaces, Bull. Carpathian J. Math., in press.         [ Links ]

[6]    E. Ekici, -preopen sets, Mathematica, Tome 47(70), No. 2, pp. 157164, (2005).         [ Links ]

[7]    K.R. Gently and H.B. Hoyle, Somewhat continuous functions, Czech-slovak Math. J., 21, pp. 5-12, (1971).         [ Links ]

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

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

[10]    S. Raychaudhuri, Concerning *-almost continuity and -preregularity, Bull. Calcutta Math. Soc., 85, pp. 385-392, (1993).

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

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

[13]    N. V. Velicko, H-closed topological spaces, Mat. Sb., 70 (1966), 98112; Englishtransl., Amer. Math. Soc. Transl., 78, pp. 103-118, (1968).         [ Links ]


Received : January 2016. Accepted : May 2016

 

M. Caldas
Departamento de Matematica Aplicada,
Universidade Federal Fluminense,
Rua Mário Santos Braga, s/no
24020-140, Niterái,

R. J. Brazil
e-mail: gmamccs@vm.uff.br

S.    Jafari
College of Vestsjaelland South,
Herrestraede 11,
4200 Slagelse,
Denmark
e-mail: jafaripersia@gmail.com

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