Chapter 10. Topology
 10.1. Topology Types
 10.2. Topology Domains
 10.3. Topology and TopoGeometry Management
 10.4. Topology Statistics Management
 10.5. Topology Constructors
 10.6. Topology Editors
 10.7. Topology Accessors
 10.8. Topology Processing
 10.9. TopoGeometry Constructors
 10.10. TopoGeometry Editors
 10.11. TopoGeometry Accessors
 10.12. TopoGeometry Outputs
 10.13. Topology Spatial Relationships
The PostGIS Topology types and functions are used to manage topological objects such as faces, edges and nodes.
Sandro Santilli's presentation at PostGIS Day Paris 2011 conference gives a good synopsis of PostGIS Topology and where it is headed Topology with PostGIS 2.0 slide deck .
Vincent Picavet provides a good synopsis and overview of what is Topology, how is it used, and various FOSS4G tools that support it in PostGIS Topology PGConf EU 2012 .
An example of a topologically based GIS database is the US Census Topologically Integrated Geographic Encoding and Referencing System (TIGER) database. If you want to experiment with PostGIS topology and need some data, check out Topology_Load_Tiger .
The PostGIS topology module has existed in prior versions of PostGIS but was never part of the Official PostGIS documentation. In PostGIS 2.0.0 major cleanup is going on to remove use of all deprecated functions in it, fix known usability issues, better document the features and functions, add new functions, and enhance to closer conform to SQLMM standards.
Details of this project can be found at PostGIS Topology Wiki
All functions and tables associated with this module are installed in a schema called
topology
.
Functions that are defined in SQL/MM standard are prefixed with ST_ and functions specific to PostGIS are not prefixed.
Topology support is build by default starting with PostGIS 2.0, and can be disabled specifying withouttopology configure option at build time as described in Chapter 2, PostGIS Installation
 getfaceedges_returntype — A composite type that consists of a sequence number and an edge number.
 TopoGeometry — A composite type representing a topologically defined geometry.

validatetopology_returntype
— A composite type that consists of an error message and id1 and id2 to denote location of error. This is the return type for
ValidateTopology
.
This section lists the PostgreSQL domains installed by PostGIS Topology. Domains can be used like object types as return objects of functions or table columns. The distinction between a domain and a type is that a domain is an existing type with a check constraint bound to it.
 TopoElement — An array of 2 integers generally used to identify a TopoGeometry component.
 TopoElementArray — An array of TopoElement objects.
 AddTopoGeometryColumn — Adds a topogeometry column to an existing table, registers this new column as a layer in topology.layer and returns the new layer_id.
 DropTopology — Use with caution: Drops a topology schema and deletes its reference from topology.topology table and references to tables in that schema from the geometry_columns table.

DropTopoGeometryColumn
— Drops the topogeometry column from the table named
table_name
in schemaschema_name
and unregisters the columns from topology.layer table.  Populate_Topology_Layer — Adds missing entries to topology.layer table by reading metadata from topo tables.
 TopologySummary — Takes a topology name and provides summary totals of types of objects in topology.
 ValidateTopology — Returns a set of validatetopology_returntype objects detailing issues with topology.
 ValidateTopologyRelation — Returns info about invalid topology relation records
 FindTopology — Returns a topology record by different means.
Adding elements to a topology triggers many database queries for finding existing edges that will be split, adding nodes and updating edges that will node with the new linework. For this reason it is useful that statistics about the data in the topology tables are uptodate.
PostGIS Topology population and editing functions do not automatically update the statistics because a updating stats after each and every change in a topology would be overkill, so it is the caller's duty to take care of that.
That the statistics updated by autovacuum will NOT be visible to transactions which started before autovacuum process completed, so longrunning transactions will need to run ANALYZE themselves, to use updated statistics. 
 CreateTopology — Creates a new topology schema and registers this new schema in the topology.topology table.
 CopyTopology — Makes a copy of a topology structure (nodes, edges, faces, layers and TopoGeometries).
 ST_InitTopoGeo — Creates a new topology schema and registers this new schema in the topology.topology table and details summary of process.
 ST_CreateTopoGeo — Adds a collection of geometries to a given empty topology and returns a message detailing success.
 TopoGeo_AddPoint — Adds a point to an existing topology using a tolerance and possibly splitting an existing edge.
 TopoGeo_AddLineString — Adds a linestring to an existing topology using a tolerance and possibly splitting existing edges/faces. Returns edge identifiers.
 TopoGeo_AddPolygon — Adds a polygon to an existing topology using a tolerance and possibly splitting existing edges/faces. Returns face identifiers.
 ST_AddIsoNode — Adds an isolated node to a face in a topology and returns the nodeid of the new node. If face is null, the node is still created.

ST_AddIsoEdge
— Adds an isolated edge defined by geometry
alinestring
to a topology connecting two existing isolated nodesanode
andanothernode
and returns the edge id of the new edge.  ST_AddEdgeNewFaces — Add a new edge and, if in doing so it splits a face, delete the original face and replace it with two new faces.
 ST_AddEdgeModFace — Add a new edge and, if in doing so it splits a face, modify the original face and add a new face.
 ST_RemEdgeNewFace — Removes an edge and, if the removed edge separated two faces, delete the original faces and replace them with a new face.
 ST_RemEdgeModFace — Removes an edge and, if the removed edge separated two faces, delete one of the them and modify the other to take the space of both.
 ST_ChangeEdgeGeom — Changes the shape of an edge without affecting the topology structure.
 ST_ModEdgeSplit — Split an edge by creating a new node along an existing edge, modifying the original edge and adding a new edge.
 ST_ModEdgeHeal — Heals two edges by deleting the node connecting them, modifying the first edge and deleting the second edge. Returns the id of the deleted node.
 ST_NewEdgeHeal — Heals two edges by deleting the node connecting them, deleting both edges, and replacing them with an edge whose direction is the same as the first edge provided.

ST_MoveIsoNode
— Moves an isolated node in a topology from one point to another. If new
apoint
geometry exists as a node an error is thrown. Returns description of move.  ST_NewEdgesSplit — Split an edge by creating a new node along an existing edge, deleting the original edge and replacing it with two new edges. Returns the id of the new node created that joins the new edges.
 ST_RemoveIsoNode — Removes an isolated node and returns description of action. If the node is not isolated (is start or end of an edge), then an exception is thrown.
 ST_RemoveIsoEdge — Removes an isolated edge and returns description of action. If the edge is not isolated, then an exception is thrown.
 GetEdgeByPoint — Finds the edgeid of an edge that intersects a given point.
 GetFaceByPoint — Finds face intersecting a given point.
 GetFaceContainingPoint — Finds the face containing a point.
 GetNodeByPoint — Finds the nodeid of a node at a point location.
 GetTopologyID — Returns the id of a topology in the topology.topology table given the name of the topology.
 GetTopologySRID — Returns the SRID of a topology in the topology.topology table given the name of the topology.
 GetTopologyName — Returns the name of a topology (schema) given the id of the topology.

ST_GetFaceEdges
— Returns a set of ordered edges that bound
aface
.  ST_GetFaceGeometry — Returns the polygon in the given topology with the specified face id.
 GetRingEdges — Returns the ordered set of signed edge identifiers met by walking on an a given edge side.
 GetNodeEdges — Returns an ordered set of edges incident to the given node.
 Polygonize — Finds and registers all faces defined by topology edges.
 AddNode — Adds a point node to the node table in the specified topology schema and returns the nodeid of new node. If point already exists as node, the existing nodeid is returned.
 AddEdge — Adds a linestring edge to the edge table and associated start and end points to the point nodes table of the specified topology schema using the specified linestring geometry and returns the edgeid of the new (or existing) edge.
 AddFace — Registers a face primitive to a topology and gets its identifier.
 ST_Simplify — Returns a "simplified" geometry version of the given TopoGeometry using the DouglasPeucker algorithm.
 CreateTopoGeom — Creates a new topo geometry object from topo element array  tg_type: 1:[multi]point, 2:[multi]line, 3:[multi]poly, 4:collection
 toTopoGeom — Converts a simple Geometry into a topo geometry.

TopoElementArray_Agg
— Returns a
topoelementarray
for a set of element_id, type arrays (topoelements).
 clearTopoGeom — Clears the content of a topo geometry.
 TopoGeom_addElement — Adds an element to the definition of a TopoGeometry.
 TopoGeom_remElement — Removes an element from the definition of a TopoGeometry.
 TopoGeom_addTopoGeom — Adds element of a TopoGeometry to the definition of another TopoGeometry.
 toTopoGeom — Adds a geometry shape to an existing topo geometry.

GetTopoGeomElementArray
— Returns a
topoelementarray
(an array of topoelements) containing the topological elements and type of the given TopoGeometry (primitive elements). 
GetTopoGeomElements
— Returns a set of
topoelement
objects containing the topological element_id,element_type of the given TopoGeometry (primitive elements).  ST_SRID — Returns the spatial reference identifier for a topogeometry.
 AsGML — Returns the GML representation of a topogeometry.
 AsTopoJSON — Returns the TopoJSON representation of a topogeometry.
 Equals — Returns true if two topogeometries are composed of the same topology primitives.
 Intersects — Returns true if any pair of primitives from the two topogeometries intersect.