Homeomorphisms with Small Twist

TL;DR

This paper extends Baumgartner's results on homeomorphisms of dense subsets of the real line, showing they can be made absolutely continuous and generalized to higher dimensions R^n.

Contribution

It introduces methods to construct absolutely continuous homeomorphisms and generalizes the results to multi-dimensional Euclidean spaces.

Findings

Homeomorphisms can be absolutely continuous.

Results extend to R^n from R.

Provides new techniques for constructing such homeomorphisms.

Abstract

We extend Baumgartner's result on isomorphisms of aleph_1 dense subsets of the reals R in two ways: First, the function can be made to be absolutely continuous. Second, one can replace R by R^n.