theorem Th35: :: NORMSP_2:35

for X, Y being RealNormSpace
for f being Function of (TopSpaceNorm X),(TopSpaceNorm Y)
for ft being Function of (LinearTopSpaceNorm X),(LinearTopSpaceNorm Y)
for x being Point of (TopSpaceNorm X)
for xt being Point of (LinearTopSpaceNorm X) st f = ft & x = xt holds
( f is_continuous_at x iff ft is_continuous_at xt )