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A note on Saleh's paper ‘Almost continuity implies closure continuity’†

Published online by Cambridge University Press:  18 May 2009

Julian Dontchev  and
Takashi Noiri
Julian Dontchev
Affiliation:
Department of Mathematics, University of Helsinki, PL4, Yliopistonkatu 15 00014 Helsinki, Finland, E-mail: dontchev@cc.helsinki.fi
Takashi Noiri
Affiliation:
Department of Mathematics, Yatsushiro College of Technology, 2627 Hirayama Shinmachi, Yatsushiro-Shi Kumanmoto-Ken 866, Japan E-mail: noiri@as.yatsushiro-nct.ac.jp
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Recently, Saleh [3] claimed to have solved ‘a long standing open question’ in topology; namely, he proved that every almost continuous function is clousure continuous (= θ = continuous). Unforunately, this problem was settled long time ago and even a better result is known. Consider the following implications: Cont. ⇒ Almost cont. ⇒ Almost α-cont.⇒ η-cont. ⇒.θ-cont. ⇒ Weakley cont.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 473
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Dickman, R.F. Jr, Porter, J.R. and Rubin, L.R., Completely regular absolutes and projective objects, Pacific J. Math., 94 (1981), 277–295.CrossRefGoogle Scholar
2.Noiri, T., Almost a-continuous functions, Kyungpook Math. J., 28 (1988), 71–77.Google Scholar
3.Seleh, M., Almost continuity implies closure continuity, Glasgow Math. J., 40 (1998), 263–264.CrossRefGoogle Scholar