The Collaborative International Dictionary of English v.0.48:

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.]
   [1913 Webster]

   2. a branch of mathematics which studies the properties of
      geometrical forms which retain their identity under
      certain transformations, such as stretching or twisting,
      which are homeomorphic. See also topologist.
      [PJC]

   3. configuration, especially in three dimensions; -- used, e.
      g. of the configurations taken by macromolecules, such as
      superhelical DNA.
      [PJC]

WordNet (r) 3.0 (2006):

topology
    n 1: topographic study of a given place (especially the history
         of the 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, topology]
    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: topology,
       analysis situs]
    4: the configuration of a communication network [syn:
       topology, network topology]

The Free On-line Dictionary of Computing (30 December 2018):

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)