On faint continuity

Aisling E. McCluskey, Ivan L. Reilly

Abstract

Recently the class of strongly faintly $\alpha$-continuous functions between topological spaces has been defined and studied in some detail. We consider this class of functions from the perspective of change(s) of topology. In particular, we conclude that each member of this class of functions belongs the usual class of continuous functions between topological spaces when the domain and codomain of the function in question have been retopologized appropriately. Some consequences of this fact are considered in this paper.


Keywords

Change of topology; strongly faint α-continuity; faint α-continuity

Subject classification

54A10; 54C08; 54C10

Full Text:

PDF

References

D. Andrijevic, On b-open sets, Mat. Vesnik 48 (1996), 59-64. https://doi.org/10.1080/00332747.1996.11024750

H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math. 8 (1964), 351-360. https://doi.org/10.1215/ijm/1256059678

J. Dugundji, Topology, Allyn and Bacon, Boston, Mass. (1966).

D. Gauld, M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, Continuity properties of functions, Coll. Math. Soc. Janos Bolyai 41 (1983), 311-322.

N. Levine, Semi open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. https://doi.org/10.1080/00029890.1963.11990039

P. E. Long and L. L. Herrington, Strongly $theta$-continuous functions, J. Korean Math. Soc. 18 (1981), 21-28.

P. E. Long and L. L. Herrington, The $T_theta$-topology and faintly continuous functions, Kyungpook Math. J. 22 (1982), 7-14.

S. N. Maheshwari and S. S. Thakur, On $alpha$-irresolute mappings, Tamkang J. Math. 11 (1980), 209-214.

R. A. Mahmoud, M. E. Abd El-Monsef and A. A. Nasef, Some forms of strongly $mu$-continuous functions, $mu in alpha$-irresolute, open, closed, Kyungpook Math. J. 36 (1996), 143-150.

A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Eygpt 53 (1982), 47-53.

A. A. Nasef, Recent progress in the theory of faint continuity, Math. Comput. Modelling 49 (2009), 536-541. https://doi.org/10.1016/j.mcm.2008.05.007

A. A. Nasef and T. Noiri, Strong forms of faint continuity, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 19 (1998), 21-28.

O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961- 970. https://doi.org/10.2140/pjm.1965.15.961

T. Noiri, On $delta$-continuous functions, J. Korean Math. Soc. 16 (1980), 161-166.

T. Noiri and V. Popa, Weak forms of faint continuity, Bull. Math. Soc. Sci. Math. R. S. Roumanie 34 (82) (1990), 263- 270.

I. L. Reilly and M. K. Vamanamurthy, On $alpha$-continuity in topological spaces, Acta Math. Hungar. 45 (1985), 27-32. https://doi.org/10.1007/BF01955019

N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78, no. 2 (1968), 103-118. https://doi.org/10.1090/trans2/078/05

Abstract Views

3586
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt