:: deftheorem Def4 defines alpha WAYBEL29:def 4 :

for X being non empty TopSpace

for b_{2} being Function of (oContMaps (X,Sierpinski_Space)),(InclPoset the topology of X) holds

( b_{2} = alpha X iff for g being continuous Function of X,Sierpinski_Space holds b_{2} . g = g " {1} );

for X being non empty TopSpace

for b

( b