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Which is the standard topology on upper semicontinuous functions and on functions of Baire class one, in both cases defined on a compact real interval?

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  • $\begingroup$ Topology on the graph of these functions? $\endgroup$
    – Dieter Kadelka
    Commented Apr 22, 2021 at 21:15
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    $\begingroup$ If you restrict to bounded functions then the uniform norm would seem pretty natural, since unless I'm mistaken it would make both spaces complete. $\endgroup$
    – Nate Eldredge
    Commented Apr 23, 2021 at 0:01

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