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1 results

  • Remarks on Two Weak Forms of Continuity

  • M. Solveig Espelie, James E. Joseph
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 1 / 01 March 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 59-63
    Print publication:
    01 March 1982
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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.