theorem Th18: :: METRIZTS:18

for TM being metrizable TopSpace
for iC being infinite Cardinal holds
( weight TM c= iC iff for Fm being Subset-Family of TM st Fm is open & Fm is Cover of TM holds
ex Gm being Subset-Family of TM st
( Gm c= Fm & Gm is Cover of TM & card Gm c= iC ) )