Geodesic
Almost Continuous Functions with Closed Graphs
Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 428-434

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DOI

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.
DOI : 10.4153/CMB-1982-061-2
Mots-clés : 54C08, 54E50, almost continuous function, complete metric space 
Berner, Andrew J. Almost Continuous Functions with Closed Graphs. Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 428-434. doi: 10.4153/CMB-1982-061-2
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     title = {Almost {Continuous} {Functions} with {Closed} {Graphs}},
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     year = {1982},
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     doi = {10.4153/CMB-1982-061-2},
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