I don’t actually know much about topology, apart from the background level, and the edge-case of graph theory. Often the coarse topology of networks is of interest, or the more metaphorical knowledge topology, or actual continuous fields or knots or whatever. Sometimes I care about the induced topology of a metric convergence, but this is hardly fancy stuff.

Apparently grown-up topology has uses too though?

For example it’s hip in machine learning. See for example

## Refs

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