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It is obvious that l is continuous on the interval because F ≠ 0. Thus the maximum value is undoubtedly one among l(2),l(N) or the extreme values of l.
For arbitrary, is continuous on the interval in the -sense.
(V_{0}) is continuous on the set (G =bar{G})).
Therefore, is continuous on the interval in the -sense.
It is also obvious that h ′ (x) is continuous on the interval.
and G ( t, s ) is continuous on the unit square [ 0, 1 ] × [ 0, 1 ].
It is obvious that n(x) is continuous on the interval.
Since is continuous on the compact interval, there is a point where attains its maximum.
We see that is continuous on the compact interval and so it is uniformly continuous.
For any (Xinmathscr{C}), (trightarrow(TX)(t)) is continuous on the interval ([0,b]) in the (L^{2} -sense.
Step 1: We first show that the mapping (trightarrow (Psi x)(t)) is continuous on the interval ([0, a]).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com