Within a Geographic Information System (GIS), which definitions correctly describe core topological relationships among spatial features?

Introduction / Context:
Topology captures the relationships among GIS features independent of their exact coordinates or scale. It enables quality control (e.g., no gaps between polygons), network analysis (e.g., routing), and spatial reasoning.

Given Data / Assumptions:

• Vector data model with points, lines, and polygons.
• Topology is invariant under continuous transformations that do not tear or glue features.
• Definitions focus on relationships, not metric distances.

Concept / Approach:
Adjacency describes which polygons share boundaries; containment identifies features wholly within others; connectivity encodes how lines join at nodes. Together these relations support tasks such as parcel adjacency checks, hydrologic tracing, and utility network flow analysis.

Step-by-Step Solution:
Map each term to its canonical GIS meaning.Recognize all three are topological, not purely geometric/metric.Conclude the inclusive option “All of these” is correct.

Verification / Alternative check:
Topology rules in GIS software enforce adjacency/containment/connection constraints during editing and validation.

Why Other Options Are Wrong:

• Claiming only connectivity matters ignores essential polygon-polygon relations fundamental to GIS topology.

Common Pitfalls:
Confusing geometric accuracy (e.g., coordinate precision) with topological correctness (e.g., shared boundaries).

Final Answer:
All of these.