public string WorkspaceName {get;}

// Asynchronously retrieves the properties of a geodatabase topology with the specified name from the given map.
var topoProperties = await activeMap.GetTopologyAsync(topologyName) as GeodatabaseTopologyProperties;

var workspace = topoProperties.WorkspaceName;
var topoLayer = topoProperties.TopologyLayer;
var clusterTolerance = topoProperties.ClusterTolerance;