Is it true that after the the metrization theorems of Bing and Nagata-Smirnov that the field is more or less dead, so there are no unsolved problems? Is it the case that any problems coming up require more structure so fall into other fields?


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  • $\begingroup$ Is real analysis dead? One could view it the other way: You need real analysis for lots of things, and you need point set topology for lots of things too. $\endgroup$ – Michael Jan 24 '17 at 6:26
  • $\begingroup$ I don't think this is quite the right way to see things. Most research is not done at the level of undergrad general topology. Most research requires a lot more than the stuff you would learn in a general topology course. $\endgroup$ – user223391 Jan 24 '17 at 6:35
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    $\begingroup$ staff.fnwi.uva.nl/j.vanmill/papers/papers1990/opit.pdf This lists some open problems in point set topology. $\endgroup$ – Pragnya Jha Jan 24 '17 at 6:35
  • $\begingroup$ @PragnyaJha It's from 1990. Kind of proves the point, I am afraid. $\endgroup$ – Felix Goldberg Mar 16 '17 at 11:14