  We propose a unifying general framework of quantitative primal and dual
sufficient and necessary error bound conditions covering linear and nonlinear,
local and global settings. The function is not assumed to possess any
particular structure apart from the standard assumptions of lower
semicontinuity in the case of sufficient conditions and (in some cases)
convexity in the case of necessary conditions. We expose the roles of the
assumptions involved in the error bound assertions, in particular, on the
underlying space: general metric, normed, Banach or Asplund. Employing special
collections of slope operators, we introduce a succinct form of sufficient
error bound conditions, which allows one to combine in a single statement
several different assertions: nonlocal and local primal space conditions in
complete metric spaces, and subdifferential conditions in Banach and Asplund
spaces.
