The code example shows the filename and path that is used by Export Topology Errors—Help | ArcGIS for Desktop
Sadly, if they aren't specified ... defaults are used
in_topology - The topology from which the errors will be exported.
Topology Layer out_path
The output workspace to which the feature classes will be created. The default is the workspace where the topology is located.
Feature Dataset; Workspace out_basename
Name to prepend to each output feature class. This allows you to specify unique output names when running multiple exports to the same workspace. The default is the topology name.