public sealed class Topology : ArcGIS.Core.Data.Dataset, System.IDisposable  

public void OpenTopologyAndProcessDefinition()
{
  // Open a geodatabase topology from a file geodatabase and process the topology definition.

  using (Geodatabase geodatabase = new Geodatabase(new FileGeodatabaseConnectionPath(new Uri(@"C:\TestData\GrandTeton.gdb"))))
  using (Topology topology = geodatabase.OpenDataset<Topology>("Backcountry_Topology"))
  {
    ProcessDefinition(geodatabase, topology);
  }

  // Open a feature service topology and process the topology definition.

  const string TOPOLOGY_LAYER_ID = "0";

  using (Geodatabase geodatabase = new Geodatabase(new ServiceConnectionProperties(new Uri("https://sdkexamples.esri.com/server/rest/services/GrandTeton/FeatureServer"))))
  using (Topology topology = geodatabase.OpenDataset<Topology>(TOPOLOGY_LAYER_ID))
  {
    ProcessDefinition(geodatabase, topology);
  }
}

private void ProcessDefinition(Geodatabase geodatabase, Topology topology)
{
  // Similar to the rest of the Definition objects in the Core.Data API, there are two ways to open a dataset's 
  // definition -- via the Topology dataset itself or via the Geodatabase.

  using (TopologyDefinition definitionViaTopology = topology.GetDefinition())
  {
    OutputDefinition(geodatabase, definitionViaTopology);
  }

  using (TopologyDefinition definitionViaGeodatabase = 
    geodatabase.GetDefinition<TopologyDefinition>("Backcountry_Topology"))
  {
    OutputDefinition(geodatabase, definitionViaGeodatabase);
  }
}

private void OutputDefinition(Geodatabase geodatabase, TopologyDefinition topologyDefinition)
{
  Console.WriteLine($"Topology cluster tolerance => {topologyDefinition.GetClusterTolerance()}");
  Console.WriteLine($"Topology Z cluster tolerance => {topologyDefinition.GetZClusterTolerance()}");

  IReadOnlyList<string> featureClassNames = topologyDefinition.GetFeatureClassNames();
  Console.WriteLine($"There are {featureClassNames.Count} feature classes that are participating in the topology:");

  foreach (string name in featureClassNames)
  {
    // Open each feature class that participates in the topology.

    using (FeatureClass featureClass = geodatabase.OpenDataset<FeatureClass>(name))
    using (FeatureClassDefinition featureClassDefinition = featureClass.GetDefinition())
    {
      Console.WriteLine($"\t{featureClass.GetName()} ({featureClassDefinition.GetShapeType()})");
    }
  }
}