Glasnik Matematicki, Vol. 40, No.2 (2005), 317-322.


Miguel Caldas and Saeid Jafari

Departamento de Mathematica Aplicada, Universidade Federal Fluminense, Rua Mario Santos Braga, s/n - CEP: 24020-140, Niteroi-RJ, Brazil

College of Vestsjaelland Syd, Herrestraede 11, 4200 Slagelse, Denmark

Abstract.   Popa introduced the notion of rare continuity. In this paper, we introduce a new class of functions called rarely g-continuous functions and investigate some of its fundamental properties. This type of continuity is a generalization of both rare continuity and weak continuity.

2000 Mathematics Subject Classification.   54B05, 54C08, 54D05.

Key words and phrases.   Rare set, g-open, rarely continuous, rarely almost compact.

Full text (PDF) (free access)

DOI: 10.3336/gm.40.2.11


  1. K. Balachandran, P. Sundaram and H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ. (Series Math.) 12 (1991), 5-13.

  2. M. Caldas, On g-closed sets and g-continuous mappings, Kyungpook Math. J. 33 (1993), 205-209.

  3. M. Caldas, S. Jafari and T. Noiri, Properties of weakly g-continuous functions, under preparation.

  4. W. Dunham, T1/2-spaces, Kyungpook Math. J. 17 (1977), 161-169.

  5. W. Dunham and N. Levine, Further results on generalized closed sets in topology, Kyungpook Math. J. 20 (1980), 164-175.

  6. S. Jafari, A note on rarely continuous functions, Univ. Bacau. Stud. Cerc. St. Ser. Mat. 5 (1995), 29-34.

  7. S. Jafari, On some properties of rarely continuous functions, Univ. Bacau. Stud. Cerc. St. Ser. Mat. 7 (1997), 65-73.

  8. N. Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly 60 (1961), 44-46.

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

  10. P. E. Long and L. L. Herrington, Properties of rarely continuous functions, Glasnik Mat. Ser. III 17(37) (1982), 147-153.

  11. V. Popa, Sur certain decomposition de la continuité dans les espaces topologiques, Glasnik Mat. Ser. III 14(34) (1979), 359-362.

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