theorem Th27: :: WAYBEL26:27

for X being non empty TopSpace
for x being Point of X
for Y being monotone-convergence T_0-TopSpace ex F being directed-sups-preserving projection Function of (oContMaps (X,Y)),(oContMaps (X,Y)) st
( ( for f being continuous Function of X,Y holds F . f = X --> (f . x) ) & ex h being continuous Function of X,X st
( h = X --> x & F = oContMaps (h,Y) ) )