[Robin_Message]

Not sure why it's called topological sort or what it had to do with topology, but it's a graph traversal where predecessors are visited before their successors. Such a sort only exists if there are no cycles in the graph.

[__MatrixMan__]

It's been a while since I took a Topology class, but I left it with the understanding that Topology is all about taking a set (nodes, say) and applying some notion of closeness (how many hops?).

Once you've done that, you have a topological space. The sets that you've defined as "close together" are your open sets. Loosely speaking, smaller open sets are considered closer together than larger ones.

This might seem boring in the case of directed graphs, which have an obvious notion of closeness, but there are more exotic spaces where you might not usually think to use "spacial" reasoning, but where it can be applied anyhow thanks to the formalism.

In a topological sort, you end up arranging the elements based on nearness to each other (as much as is possible for a list), so that elements in a given open set in the typical topological space over directed graphs are likely to be next to each other in the list. It's a pretty topological way to do things, which probably explains the name.