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Remarks on Two Weak Forms of Continuity
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1982
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