This is roughly how my analysis prof explained the birth of topology: removing the properties of space, layer by layer, until you’re left with only the bare necessities required to do analysis (i.e. define limits)– the concept of ‘open neighborhood’ essentially. But I don’t know if that’s actually accurate historically
Insisting on a historical development cripples education, destroys history, or both: It prevents a more logical development of the topic from being used, and it does great violence to history by paring it down into something a course specialized on some other topic can digest without serious diversions.
Well I agree, but I don’t really see how that’s relevant to what I said. This was just something that my prof. mentioned. I’d single out the course itself as probably the most sensibly constructed one I’ve ever attended, and in line with the idea that you should present the logic of the thing the best you can and not focus on the history much.