set X = {(Int KurExSet ),(Int (Cl KurExSet )),(Int (Cl (Int KurExSet )))};
set Y = {(Cl KurExSet ),(Cl (Int KurExSet )),(Cl (Int (Cl KurExSet )))};
assume {(Int KurExSet ),(Int (Cl KurExSet )),(Int (Cl (Int KurExSet )))} meets {(Cl KurExSet ),(Cl (Int KurExSet )),(Cl (Int (Cl KurExSet )))} ; :: thesis: contradiction
then consider x being set such that
A1: ( x in {(Int KurExSet ),(Int (Cl KurExSet )),(Int (Cl (Int KurExSet )))} & x in {(Cl KurExSet ),(Cl (Int KurExSet )),(Cl (Int (Cl KurExSet )))} ) by XBOOLE_0:3;
( x is non empty open Subset of R^1 & x is closed Subset of R^1 ) by A1, Th50, ENUMSET1:def 1;
hence contradiction by A1, Th52, BORSUK_5:57; :: thesis: verum