Unions of Rectifiable Curves and the Dimension of Banach Spaces

Details Unions of Rectifiable Curves and the Dimension of Banach Spaces Unions of Rectifiable Curves and the Dimension of Banach Spaces

1996-02-20

arxiv.org/abs/math/9602205v1

Mathematics

Logic

Scientific paper

To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that that any set of reals of size $\aleph_1$ is meagre yet therer are $\aleph_1$ rectifiable curves in $\Reals^3$ whose union is not meagre. The consistency of this statement when the phrase ``rectifiable curves'' is replaced by ``straight lines'' remains open.

Affiliated with

Also associated with

No associations

Rating

Unions of Rectifiable Curves and the Dimension of Banach Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unions of Rectifiable Curves and the Dimension of Banach Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unions of Rectifiable Curves and the Dimension of Banach Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-438189