  In this paper, we suggest a mathematical representation to the holographic
principle through the theory topological retracts. We found that the
topological retraction is the mathematical analogs of the hologram idea in
modern quantum gravity and it can be used to explore the geometry of the
hologram boundary. An example has been given on the five dimensional (5D)
wormhole space-time $W$ which we found it can retract to lower dimensional
circles $S_i \subset W$. In terms of the holographic principle, the description
of this volume of space-time $W$ is encoded on the lower-dimensional circle
which is the region boundary.
