tag:blogger.com,1999:blog-11295132.post5859707800583893899..comments2014-08-17T09:30:19.334-07:00Comments on A Neighborhood of Infinity: A pictorial proof of the hairy ball theoremDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-11295132.post-86671348688420557272012-12-01T11:36:40.975-08:002012-12-01T11:36:40.975-08:00A typical constructive variant of this sort of the...A typical constructive variant of this sort of theorem would be say that for every epsilon there is a vector whose magnitude is less than epsilon, which is usually strong enough to work with.Russell O'Connorhttps://roconnor.myopenid.com/noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-13494761668579086752012-11-18T20:39:00.577-08:002012-11-18T20:39:00.577-08:00I was thinking about constructive versions of this...I was thinking about constructive versions of this when I hinted that there's a procedure for searching for zeros based on computing winding numbers around various regions. Like the intermediate value theorem I'd expect it to fail in a constructively. But many of these kinds of results have discrete versions that I suspect do still work constructively and there may be a version of this winding number argument that still works in that case.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-42379679847805735182012-11-18T19:17:56.568-08:002012-11-18T19:17:56.568-08:00I bet this theorem fails in the effective topos, w...I bet this theorem fails in the effective topos, where there is a continuous map on the disc which has no fixed points (so it violates Brouwer's fixed point theorem).Andrej Bauerhttp://andrej.com/noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-87694540666275813112012-11-18T19:16:12.540-08:002012-11-18T19:16:12.540-08:00This comment has been removed by the author.Profesor Umnikhttp://www.blogger.com/profile/03377063988492869441noreply@blogger.com