Timeline for What is the pure intuition for topological continuity and topology? [closed]
Current License: CC BY-SA 2.5
17 events
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| Nov 14, 2021 at 19:57 | comment | added | Yemon Choi | @PineappleFish I also have a feeling that at the time, this particular question came among a wave of others which had a similar agenda, which did not predispose me to sympathy. Finally, I think I was rather restrained in my comment; those who wish to find answers rather than win rhetorical points should learn to adjust how they speak, in much the same way that I don't talk to my UG students the way I talk to my friends in the pub | |
| Nov 14, 2021 at 19:52 | comment | added | Yemon Choi | @PineappleFish Thank you for your considered remarks. All I can say is that 10 years ago both MathOverflow and I were rather different, and certainly 10 years ago there was more of a feel of a small group of like-minded enthusiasts rather than a sense of communal responsibility. My comment was made in the context of a certain kind of fevered blogging style online whereby people would seem to think it is acceptable and admirable to disparage epsilon-delta and traditional analysis because someone more famous has made similar disparagements. | |
| Nov 14, 2021 at 5:47 | comment | added | Pineapple Fish | @YemonChoi people ask questions because they are frustrated. Probably more so because they are willing to ask about it online. I know because I speak from experience. Because this post does not attack any user in particular, I ask that you do not be so harsh to the original poster. I understand and agree with your comment [and better to leave one than not, btw ;)], but these are the kinds of comments that just make the student feel even worse and really don't contribute to anything. The comment is fine, I'm just saying that after reading the post, it feels like adding insult to injury. | |
| Jul 2, 2010 at 0:11 | comment | added | Yemon Choi | -1 for the combination of florid style and snark. | |
| Jul 1, 2010 at 21:50 | history | edited | Nick | CC BY-SA 2.5 |
addition of thank note
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| Jul 1, 2010 at 21:14 | comment | added | Pietro Majer | I think it would be a nice policy to start a count down before closing a question. This way a contributor would avoid loosing his/her time in writing a useless answer. | |
| Jul 1, 2010 at 21:08 | comment | added | lhf | See also this discussion: mathoverflow.net/questions/19152/… | |
| Jul 1, 2010 at 21:08 | history | closed |
Robin Chapman Harry Gindi Charles Siegel Harald Hanche-Olsen Yemon Choi |
not constructive | |
| Jul 1, 2010 at 21:01 | answer | added | Robin Saunders | timeline score: 1 | |
| Jul 1, 2010 at 20:31 | comment | added | Robin Chapman | For a motivation for topology from a different source from geometry, you might see the book Topology via Logic by Steven Vickers (CUP 1989). | |
| Jul 1, 2010 at 20:30 | comment | added | Mariano Suárez-Álvarez | Your question is strange because it seems to assume that concepts jump out of thing air, independently of examples. Quite the contrary: the notions of continuity is an abstraction of the observed fact that some of the functions people had interest were continuous. Continuous functions very much preceded the definition of continuity! | |
| Jul 1, 2010 at 20:26 | comment | added | Charles Siegel | But it IS the epsilon-delta. It's a theorem in $\epsilon-\delta$ theory of continuity that the inverse image of an open set is open. Then, at some point, you start to encounter geometric objects without obvious metrics...so you need a notion of continuity that doesn't require the metric. Thus, the theorem becomes the definition. | |
| Jul 1, 2010 at 20:26 | comment | added | Mariano Suárez-Álvarez | Also, the expression "unbiased motivation" is quite intriguing! | |
| Jul 1, 2010 at 20:21 | comment | added | Andy Putman | This is a strange question. You want us to motivate the most general notion of continuity without appealing to our intuition for spaces like R^n; however, that is precisely the correct motivation! Maybe some people will have other opinions, but I'm pretty sure that most mathematicians use specific and concrete things (like R^n) to motivate definitions and results concerning abstract things (like topological spaces). Why would you want to do otherwise? | |
| Jul 1, 2010 at 20:20 | comment | added | Qiaochu Yuan | There's been a long discussion about these kinds of issues here: mathoverflow.net/questions/19152/… . Several of the answers are quite enlightening. | |
| Jul 1, 2010 at 20:19 | comment | added | Robin Chapman | But we do know the notion of epsilon-delta continuity. | |
| Jul 1, 2010 at 20:16 | history | asked | Nick | CC BY-SA 2.5 |