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[138] A function \(f:Xβ β\) is said lower semicontinuous (abbreviated l.s.c.) if
\[ β x_ 0β D(X) \quad ,\quad \liminf _{xβ x_ 0} f(x)β₯ f(x_ 0) \]
and vice versa it says upper semicontinuous (abbreviated u.s.c.) if
\[ β x_ 0β D(X) \quad ,\quad \limsup _{xβ x_ 0} f(x)β€ f(x_ 0)~ . \]
(\(D(X)\) are the accumulation points in \(X\)).
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- semicontinuous, upper , see
upper semicontinuous
- semicontinuous, lower , see
lower semicontinuous
- l.s.c. , see
lower semicontinuous
- u.s.c. , see
lower semicontinuous
- lower semicontinuous
- upper semicontinuous
- accumulation point
- lower semicontinuous
- upper semicontinuous
