Timeline for Differential Topology over $\mathbb{Q}$

6 events

when toggle format	what		by	license	comment
May 24, 2015 at 18:03	comment	added	Simon Henry		If a finite union of balls contains all the rational number of the unit ball then the union of the corresponding closed ball contains all of the unit ball, so the volume of the unit ball is smaller than the sum of the volume of the ball involved in the covering. So if you take the volume of the ball in the covering to decrease fast enough so that the sum of there volume is smaller than the volume of the initial ball then any finite familly of those balls cannot form a covering of the (rationals in the) initial ball.
May 24, 2015 at 16:56	comment	added	Asaf Shachar		Can you please explain the last part in your argument. How can you prove a finite family of such balls cannot cover the initial ball? (what exactly is the volume argument?)
May 24, 2015 at 16:50	vote	accept	Asaf Shachar
May 22, 2015 at 7:50	history	edited	Simon Henry	CC BY-SA 3.0	added 377 characters in body
May 21, 2015 at 15:09	history	edited	Simon Henry	CC BY-SA 3.0	added 238 characters in body
May 21, 2015 at 15:01	history	answered	Simon Henry	CC BY-SA 3.0