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

theorem Th39:
  TrivDecomp X is u.s.c._decomposition of X
proof
  thus for A being Subset of X st A in TrivDecomp X for V being a_neighborhood
of A ex W being Subset of X st W is open & A c= W & W c= V & for B being Subset
  of X st B in TrivDecomp X & B meets W holds B c= W by Lm1;
end;
