I've lately been told that the subject of general topology, like what Hausdorff and Kolmogorov dealt with, is a a dead subject research wise. I have been wondering however whether this is indeed true, and would like to know whether there are people actively researching general topology or adjacent subjects? I would appreciate perhaps some concrete examples of people or institutions dealing with the subject.
2026-03-25 19:05:26.1774465526
Active research on the subject of general topology
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Look in the library for a copy of Open Problems in Topology (two volumes so far), and Recent Progress in General Topology (2 volumes, last from 2002) and see that it is far from dead... Most of the problems in them are still open AFAIK. Elliott Pearl has some overview papers keeping track of which ones are solved or open IIRC.
The 1990 first book of Open Problems can be found here
A first status report is here
Publisher's link for the second volume of Open Problems is here
Second volume for Recent Progress: here
etc etc. The most relevant journal is "Topology and its Applications", and there is a journal just on questions called "Questions and Answers in General Topology" (though I rarely see it any more, it was Japanese, IIRC), and Fundamenta Mathematica has many general topology papers (mostly descriptive set theory and set-theoretic).
Many people think it's dead because it's not considered interesting, or "deep", but I disagree.