🚀 go-pugleaf

                                            11-4-92

   In my posting  "Abian gives examples for Pratt"  with

    Message ID:   <abian.720807204@pv343f.vincent.iastate.edu>

     in  the  DEFINITION

                   n+1     should be     n+k     (for a suitable k)

   So, MY DEFINITION is:

      An n-dimensional differentiable manifold  M  is a connected
 subdomain of  an  n+k  dimensional  Euclidean space such that
 at every point,   M  has an n-dimensional tangent hyperplane.
      

   Also, in
   
    Message ID:    <abian.720839289@pv343f.vincent.iastate.edu>


    in  (iv)

           "for every  u, v, w "  is redundant   (although not false)

    

   So,  (iv) should read:

   (iv)  Is  H  a  one-to-one mapping ?  Yes, since the above equations are
         uniquely solvable in  x, y, z.


                                          Alexander Abian                                          

-- 
   The tendency of maintaining the status-quo, Reaction to provocation and
                The tendency of maintaining again a status-quo.  
    TIME HAS INERTIA  and some energy is lost to move Time forward  
  E = mcc  (Einstein)    must be replaced by    E = m(0) exp(-At) (Abian)