  We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS)
space. We map the Poincare AdS boundary to the global coordinate chart and show
why this boundary is not equivalent to the global AdS boundary. The Poincare
AdS boundary is shown to contain points of the bulk of the entire AdS space.
The Euclidean AdS space is also discussed. In this case one can define a
semi-global chart that divides the AdS space in the same way as the
corresponding Euclidean Poincare chart.
