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Comment by spekcular | Hacker News Reader

I guess it's worth pointing out that when mathematicians today use the word "topology" in conversation, they almost universally mean "algebraic topology." Point-set topology is as dead as the dodo.

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Pure point-set topology is as "dead" as group theory.

That is to say it's an essential part of the foundations of theoretical mathematics (you can't understand algebraic topology without understanding point-set topology), but there is not much new innovation purely within point-set topology itself.

So I find "dead as a dodo" too strong of a metaphor.

maybe as a research field, but point set topology is a basic foundation of most mathematics

I dont think so. Topology is ubiquitous in mathematics. From Zariski topologies and Stone spaces, to concrete objects like manifolds and topological vector spaces.

Where on earth did you get that idea?

The most common meaning of the word "topology" is quite simply "a topology". As in a set of opens for a particular space of interest. These show up all over the place regardless of whether you can do some algebra on them.

I meant as a field of research. Obviously the concept of an open set, etc., remain foundational.

Judging from the replies you're getting I think "field of research" was an important qualifier hahah

> Point-set topology is as dead as the dodo.

What makes it dead?

No one publishes on it anymore. My impression is that all the interesting problems are solved. I also can't think of any professor at, say, an R1 university that works primarily on point-set topology.

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