 Upper semicontinuity (source code)

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= Upper semicontinuity
{title2=$\{x:f(x)<a\}\text{ is open for every }a\in\mathbb R$}

= Upper semicontinuous
{synonym}

A real or extended-real <function> is <upper semicontinuous> when every strict sublevel set is open. Equivalently its negative is <lower semicontinuous>. An arbitrary infimum of continuous <functions> is <upper semicontinuous>, even when the infimum is over an uncountable family; its strict sublevel sets are unions of the corresponding open sublevel sets.

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