:: deftheorem defines T_0TSP_1:def 8 : for Y being TopStruct for IT being Subset of Y holds ( IT is T_0 iff for x, y being Point of Y st x in IT & y in IT & x <> y & ( for V being Subset of Y holds ( not V is open or not x in V or y in V ) ) holds ex W being Subset of Y st ( W is open & not x in W & y in W ) );