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On \(\alpha\)-continuity in topological spaces. (English) Zbl 0576.54014

In this paper \(\alpha\)-continuity, \(\alpha\)-open functions, and \(\alpha\)- closed functions, which were introduced in 1983 by A. Mashhour, I. Hasanein, and S. El-Deeb [Acta Math. Hung. 41, 213-218 (1983; Zbl 0534.54006)], and \(\alpha\)-irresolute functions, which were introduced in 1980 by S. Maheshwari and S. Thakur [Tamkang J. Math. 11, 209-214 (1981; Zbl 0485.54009)] are further investigated. The authors retopologize the domain space and/or range space to characterize \(\alpha\)-continuity using continuity, \(\alpha\)-open using open, \(\alpha\)- closed using closed, and \(\alpha\)-irresolute using continuity and these new characterizations are used to quickly establish many known properties of \(\alpha\)-continuous, \(\alpha\)-open, \(\alpha\)-closed, and \(\alpha\)- irresolute functions.
Reviewer: Ch.Dorsett

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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References:

[1] N. Levine, Semi-open sets and semi-continuity in topological spaces,Amer. Math. Monthly,70 (1963), 36–41. · Zbl 0113.16304
[2] S. N. Maheshwari and S. S. Thakur, On {\(\alpha\)}-irresolute mappings,Tamkang J. Math.,11 (1980), 209–214.
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