4 ms·

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

• Igelau 6y ago
  > Point-set topology is as dead as the dodo. What makes it dead?
  • spekcular 6y ago
    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.
• gmadsen 6y ago
  maybe as a research field, but point set topology is a basic foundation of most mathematics
• dwohnitmok 6y ago
  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.
• contravariant 6y ago
  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.
  • spekcular 6y ago
    I meant as a field of research. Obviously the concept of an open set, etc., remain foundational.
    • michaelpb 6y ago
      Judging from the replies you're getting I think "field of research" was an important qualifier hahah
• chobytes 6y ago
  I dont think so. Topology is ubiquitous in mathematics. From Zariski topologies and Stone spaces, to concrete objects like manifolds and topological vector spaces.