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 object such that
A1: x in {(Int KurExSet),(Int (Cl KurExSet)),(Int (Cl (Int KurExSet)))} and
A2: 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, A2, Th48, ENUMSET1:def 1;
hence contradiction by A1, Th49, BORSUK_5:34; :: thesis: verum