diff --git a/cpp/dolfinx/mesh/Topology.cpp b/cpp/dolfinx/mesh/Topology.cpp
index 451965634fd..0c688e24753 100644
--- a/cpp/dolfinx/mesh/Topology.cpp
+++ b/cpp/dolfinx/mesh/Topology.cpp
@@ -773,7 +773,8 @@ Topology::Topology(
   // Cell Types
   _entity_types.insert(_entity_types.end(), cell_types.begin(),
                        cell_types.end());
-  _entity_type_offsets.push_back(_entity_types.size());
+  if (tdim > 0)
+    _entity_type_offsets.push_back(_entity_types.size());
 
   std::int8_t conn_size = _entity_type_offsets.back();
   _index_map.resize(conn_size);
diff --git a/python/test/unit/mesh/test_mesh.py b/python/test/unit/mesh/test_mesh.py
index e620e1c0569..7d721f1d4f7 100644
--- a/python/test/unit/mesh/test_mesh.py
+++ b/python/test/unit/mesh/test_mesh.py
@@ -522,6 +522,7 @@ def test_submesh_full(d, n, codim, marker, ghost_mode, simplex):
     edim = max(mesh.topology.dim - codim, 0)
     entities = locate_entities(mesh, edim, marker)
     submesh, entity_map, vertex_map, geom_map = create_submesh(mesh, edim, entities)
+    assert submesh.topology.dim == edim
     submesh_topology_test(mesh, submesh, entity_map, vertex_map, edim)
     submesh_geometry_test(mesh, submesh, entity_map, geom_map, edim)