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1 results

  • Almost Continuous Functions with Closed Graphs

  • Andrew J. Berner
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 4 / 01 December 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 428-434
    Print publication:
    01 December 1982
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  • A function f:X → Y is almost continuous if for every x ∊ X and for each open set V ⊂ Y containing f(x), Cl(f-l(V)) is a neighborhood of x. Various conditions are given that guarantee that an almost continuous function is continuous. The main theorem states that if f:X → Y is almost continuous with a closed graph (closed in X × Y) and X and Y are complete metric spaces, then f is continuous.