  We show that some properties of log canonical centers of a log canonical pair
(X,D) also hold for certain subvarieties that are close to being a log
canonical center. As a consequence, we obtain that if one works with
deformations of pairs (X, D) where all the coefficients of D are bigger than
1/2, then one need not worry about embedded points on D.
  May 20: Results strengthened using recent work of Birkar and Hacon and Xu.
