public abstract class TopologyProperties 

QueuedTask.Run(async () =>
{
  var map = MapView.Active.Map;
  //Get a list of all the available topologies for the map
  var availableTopologies = await map.GetAvailableTopologiesAsync();

  var gdbTopologies = availableTopologies.OfType<GeodatabaseTopologyProperties>();
  var mapTopologies = availableTopologies.OfType<MapTopologyProperties>();
});

var map = MapView.Active.Map;
var activeTopologyProperties = await map.GetActiveTopologyAsync();
var isMapTopology = activeTopologyProperties is MapTopologyProperties;
var isGdbTopology = activeTopologyProperties is GeodatabaseTopologyProperties;
var isNoTopology = activeTopologyProperties is NoTopologyProperties;