theorem Th17: :: NORMSP_2:17

for X being RealNormSpace
for U being Subset of X
for Ut being Subset of (TopSpaceNorm X)
for x being Point of X
for xt being Point of (TopSpaceNorm X) st U = Ut & x = xt holds
( U is Neighbourhood of x iff Ut is a_neighborhood of xt )