theorem Th7: :: WEIERSTR:7

for T, S being non empty TopSpace
for f being Function of T,S
for P being Subset of T
for F being Subset-Family of S st ex B being Subset-Family of T st
( B c= f " F & B is Cover of P & B is finite ) holds
ex G being Subset-Family of S st
( G c= F & G is Cover of f .: P & G is finite )