What? Everything about this comment is wrong.
> "Topology ignores such things as corners, distances, and convexity."
No, that's what topology is.
> "That makes it hard to combine with GIS systems."
No, GIS systems rely heavily on topology. Here are two definitions:
Topology: 1. the study of geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.
Topography: 1. the arrangement of the natural and artificial physical features of an area.