assume the carrier of (VeroneseSpace S) is Block of (VeroneseSpace S) ; :: according to PENCIL_1:def 5 :: thesis: contradiction
then consider t being set , l being Subset of S such that
A1: t in the carrier of S and
A2: l in the topology of S and
A3: PairSet the carrier of S = PairSet t,l by Def10;
not the carrier of S in the topology of S by PENCIL_1:def 5;
then not the carrier of S c= l by A2, XBOOLE_0:def 10;
then consider s being set such that
A4: s in the carrier of S and
A5: not s in l by TARSKI:def 3;

now

assume {t,s} in PairSet t,l ; :: thesis: contradiction
then A6: ex z being set st
( z in l & {t,s} = {t,z} ) by Def9;
then s = t by A5, ZFMISC_1:10;
hence contradiction by A5, A6, ZFMISC_1:10; :: thesis: verum

end;

hence contradiction by A1, A3, A4, Def8; :: thesis: verum