Source : Webster's Revised Unabridged Dictionary (1913)

Topology \To*pol"o*gy\, n. [Gr. ? place + -logy.]
   The art of, or method for, assisting the memory by
   associating the thing or subject to be remembered with some
   place. [R.]

Source : WordNet®

topology
     n 1: topographic study of a given place (especially the history
          of place as indicated by its topography); "Greenland's
          topology has been shaped by the glaciers of the ice age"
     2: the study of anatomy based on regions or divisions of the
        body and emphasizing the relations between various
        structures (muscles and nerves and arteries etc.) in that
        region [syn: {regional anatomy}, {topographic anatomy}]
     3: the branch of pure mathematics that deals only with the
        properties of a figure X that hold for every figure into
        which X can be transformed with a one-to-one
        correspondence that is continuous in both directions [syn:
         {analysis situs}]
     4: the configuration of a communication network [syn: {network
        topology}]

Source : Free On-Line Dictionary of Computing

topology
     
        1.  The branch of mathematics dealing with
        {continuous transformations}.
     
        2.  Which {hosts} are directly connected to which
        other hosts in a {network}.  {Network layer} processes need to
        consider the current network topology to be able to {route}
        {packets} to their final destination reliably and efficiently.
     
        (2001-03-29)