Timeline for Can all contours of a function on a disk be made arbitrarily small?

Current License: CC BY-SA 3.0

14 events

when toggle format	what		by	license	comment
Apr 24, 2018 at 0:37	vote	accept	Alexander Gelbukh
Apr 23, 2018 at 22:01	answer	added	Irina		timeline score: 9
S Apr 23, 2018 at 14:49	history	suggested	Menachem	CC BY-SA 3.0	Added the "continuous" restriction earlier on in the question.
Apr 23, 2018 at 13:31	review	Suggested edits
S Apr 23, 2018 at 14:49
Apr 23, 2018 at 1:41	comment	added	fedja		For a simple Morse function, consider the contour at the level $f(0)$ passing through $0$. If it reaches the boundary, you are done. Otherwise it bounds some domain. Move the level so that this domain is expanding and consider the first moment it reaches the boundary (possibly by merging with another domain). Shortly before or shortly after that moment you should have what you want.
Apr 22, 2018 at 23:55	history	edited	Alexander Gelbukh	CC BY-SA 3.0	added 5 characters in body
Apr 22, 2018 at 21:28	history	edited	Alexander Gelbukh	CC BY-SA 3.0	added 30 characters in body
Apr 22, 2018 at 21:12	history	edited	Alexander Gelbukh	CC BY-SA 3.0	added 4 characters in body
Apr 22, 2018 at 21:06	history	edited	Alexander Gelbukh	CC BY-SA 3.0	added 4 characters in body
Apr 22, 2018 at 20:57	history	edited	Alexander Gelbukh	CC BY-SA 3.0	added 4 characters in body
Apr 22, 2018 at 20:47	history	edited	Alexander Gelbukh	CC BY-SA 3.0	added 11 characters in body
Apr 22, 2018 at 20:45	comment	added	Alexander Gelbukh		@NateEldredge Right, will edit the question.
Apr 22, 2018 at 20:39	comment	added	Nate Eldredge		At a minimum you need $f$ to be continuous or something. Without any other assumptions you can choose an $f$ which is injective, and then every contour is a single point and has diameter zero.
Apr 22, 2018 at 20:15	history	asked	Alexander Gelbukh	CC BY-SA 3.0