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Remarks on Two Weak Forms of Continuity

Published online by Cambridge University Press:  20 November 2018

M. Solveig Espelie  and
James E. Joseph
M. Solveig Espelie
Affiliation:
Department of Mathematics Howard University, Washington D.C. 20059
James E. Joseph
Affiliation:
Department of Mathematics Howard University, Washington D.C. 20059
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Abstract

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New characterizations of weakly-continuous and θ-continuous functions are presented, and θ-continuity is applied to characterize H(i) spaces; a recent characterization of closed graph functions is utilized to characterize H-closed spaces. Noiri has shown that a function λ which is almost-continuous in the sense of Husain is weakly-continuous if cl(λ−1(W)) ⊂ λ−1(cl(W)) for all open W. It is established here that almost-continuity is superfluous in this statement.

Keywords

54C0554D25θ-continuityweak-continuityH-closed spaces

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 59 - 63
Copyright
Copyright © Canadian Mathematical Society 1982

References

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