In Japan, there are many universities with a formal course about topological group using the classic by Pontryagin. Yet topological group is not studied in a formal course in many other countries, since it's considered as optional and less important than other topics such as Lie group. But why?
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asked Jan 20, 2015 at 20:00
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1$\begingroup$ Personally, because I think that, in general (at least for mathematics and physics), it really is less important, and perhaps even less interesting, than Lie groups. Of course, studying the latter forces you to learn something about the former. $\endgroup$– TimbucCommented Jan 20, 2015 at 20:30
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3$\begingroup$ If you are looking for an area of math that cares about topological groups that are not necessarily Lie groups, look to number theory and representation theory ($p$-adic groups, adele groups, infinite Galois groups,...). The development of analysis on general locally compact groups, by Weil, was motivated by such topological groups in number theory. $\endgroup$– KCdCommented Jan 20, 2015 at 20:48
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$\begingroup$ I see. Then, I will rather study more interesting topics like Lie groups and their branches than reading Pontryagin's book, since it should be better investment of time. I'm interested in both number theory and rep theory, so I will definitely look into such topics. Thanks for both! $\endgroup$– Math.StackExchangeCommented Jan 20, 2015 at 22:09
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