reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem Th4:
  for X being non empty TopSpace, A,B being Subset of X, U being
  a_neighborhood of B st A c= B holds U is a_neighborhood of A
proof
  let X be non empty TopSpace;
  let A,B be Subset of X, U be a_neighborhood of B such that
A1: A c= B;
  B c= Int U by CONNSP_2:def 2;
  hence A c= Int U by A1;
end;
