After creating and populating a topology, the information is stored in multiple database tables. Luckily, PostGIS has a function for getting synthetic information about a given topology and its components: it's called topology.TopologySummary. It accepts one argument, the name of the topology in question:
SELECT topology.TopologySummary('my_topology');
topologysummary
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Topology my_topology (id 2, SRID 4326, precision 0.00028)
4567 nodes, 4765 edges, 4257 faces, 255 topogeoms in 1 layers
Layer 1, type Polygonal (3), 255 topogeoms
Deploy: public.countries.topogeom
(1 row) In return, the function will print out the topology metadata (ID, SRID, and precision), the number of topology elements of each type, the number of layers, their ID, the geometry type, and the number of features in each layer.
Topology metadata can also be retrieved individually...