reserve Y for TopStruct;

theorem
  for Y being non empty TopStruct, Y0 be 1-element SubSpace of Y
holds ex y being Point of Y st the TopStruct of Y0 = the TopStruct of Sspace(y)
proof
  let Y be non empty TopStruct, Y0 be 1-element SubSpace of Y;
  consider y0 being Element of Y0 such that
A1: the carrier of Y0 = {y0} by TEX_1:def 1;
  the carrier of Y0 is Subset of Y by Lm1;
  then reconsider y = y0 as Point of Y by A1,ZFMISC_1:31;
  take y;
  the carrier of Y0 = the carrier of Sspace(y) by A1,Def2;
  hence thesis by TSEP_1:5;
end;
