Which of the following is/are topological relationship element(s) in GIS?
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Think about the arc-node GIS data model and which relationships are explicitly stored with every arc and polygon (neighbor, network link, enclosure) versus which relationship is only computed on demand from geometry.
Step 1: Recall the arc-node topological data model. Classical vector GIS software, such as the arc-node coverage model, stores geographic features not as isolated shapes but as a network of nodes and arcs with explicit relationship records attached, so that spatial relationships can be looked up instead of recomputed from coordinates every time.
Step 2: Map each stored relationship to its name. The left-polygon/right-polygon record attached to every arc encodes which two polygons are neighbors across that boundary, this relationship is called adjacency. The from-node/to-node record attached to every arc encodes how arcs link up into a connected network, this relationship is called connectivity, and it is what lets a GIS trace a continuous path along a road or stream network. A separate polygon-in-polygon or point-in-polygon record, built by testing enclosure, encodes which features lie completely inside which polygons, this relationship is called containment (or enclosure).
Step 3: Consider intersection separately. Intersection is the result of overlaying the geometries of two features and computing their common region or crossing points. Any two features, whether or not they are adjacent, connected, or contained, can be intersected purely from their coordinates, this is a computational overlay operation performed on demand, not a relationship element that the topological structure itself stores or is defined by.
Step 4: Conclusion. Because the topological data model is built specifically around the three stored relationships of adjacency, connectivity, and containment, and treats intersection as a separate computed overlay operation, the correct topological relationship elements are adjacency, connectivity and containment.
