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

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.