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Topology describes non-metric relationships among geometric figures, such as adjacency, containment, and orientation. It is a branch of Mathematics, which deals in geometry without measurement.

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Getting topology or out of memory errors with large dataset intersects and spatial joins in ...

If doing a JOIN using the ONLY_FID option works, and your dataset is unlikely to grow significantly, that is you best bet. If not, you might be back to the old fun of tiling your dataset, processing, …
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