let X be non empty TopSpace; :: thesis: ( ( for A being Subset of X holds Int A = A ) implies X is discrete )
assume A1: for A being Subset of X holds Int A = A ; :: thesis: X is discrete
now :: thesis: for A being Subset of X holds A is open
let A be Subset of X; :: thesis: A is open
Int A = A by A1;
hence A is open ; :: thesis: verum
end;
hence X is discrete by TDLAT_3:15; :: thesis: verum