Construction of Lakes of Wada

Question

At each step of the construction of Lakes of Wada we extend a lake (an open set in the open unit square) so that no point of the land (the complement of all the lakes) is farther than a given small positive number (depending on the step) from the lake and the interior of the remaining land stays connected.

How can it be rigorously shown that this kind of extended lake exists?

BAYMAX · Answer 1 · 2017-03-25T17:20:59.843

2

If you want to know more about the Lakes of Wada you can refer research articles, but here is what I found in Mathoverflow

Just refer the link,it contains various nice links -

http://www.mathoverflow.net/questions/24903/algorithms-for-the-lakes-of-wada

If the link doesnot open,we can try the following links-

1)http://www.ams.org/notices/200601/fea-coudene.pdf

2)http://www.cut-the-knot.org/do_you_know/brouwer.shtml

Hope this helps!

edited Mar 25 '17 at 17:20

answered Mar 25 '17 at 15:58

BAYMAX

4,972

I'm not sure I see the value of this answer. – pjs36 Mar 25 '17 at 16:23
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The link to the article given on the MathOverflow page is broken, but this link works: http://www.ams.org/notices/200601/fea-coudene.pdf – John Gowers Mar 25 '17 at 16:26
@JohnGowers, don't know why but the link opens in my system,and in the page this link is also included. – BAYMAX Mar 25 '17 at 17:07
@BAYMAX I edited it on the MathOverflow answer. – John Gowers Mar 25 '17 at 17:18
Ok,nice work ! still I have added the further links one will face while going deep through the pages! @JohnGowers – BAYMAX Mar 25 '17 at 17:23

Construction of Lakes of Wada

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