most recent 30 from http://mathoverflow.net 2013-05-22T10:46:08Z http://mathoverflow.net/feeds/question/33928 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/33928/a-question-about-connected-inner-limiting-sets Garabed Gulbenkian 2010-07-30T18:30:11Z 2011-11-04T15:22:12Z

<p>Let M be a finite-dimensional Euclidean space or an infinite-dimensional separable Banach space. An inner limiting subset of M is a countable intersection of open subsets of M-these sets are usually called "G-delta" sets nowadays. Does every infinite connected inner limiting subset of M contain an infinite connected proper subset H and a point p that is not a limit point of H?</p>

http://mathoverflow.net/questions/33928/a-question-about-connected-inner-limiting-sets/38222#38222 Gerhard Paseman 2010-09-09T19:54:51Z 2010-09-09T19:54:51Z

<p>This is only a partial answer.</p> <p>If M has a subset that is somewhere locally path-connected, then yes. Otherwise, M is nowhere path connected, and this should put some interesting restrictions on M. Even in this case I do not see where M could nontrivially avoid all tuples (p,O) where p is a point and O a basis element of the space that does not contain p in its closure.</p> <p>Gerhard "Ask Me About System Design" Paseman, 2010.09.09</p>