- A generalization of the Open Mapping Theorem and a possible generalization of the Baire Category Theorem(arXiv)
Author : Antoni Machowski
Abstract : We characterize continuum as the smallest cardinality of a family of compact sets needed to cover a locally compact group for which the Open Mapping Theorem does not hold.
2.Third order open mapping theorems and applications to the end-point map (arXiv)
Abstract : This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a finite dimensional manifold. In a second step, we compute the third order term in the Taylor expansion of the end-point map and we specialize the abstract theory to the study of length-minimality of sub-Riemannian strictly singular curves. We conclude with the third order analysis of a specific strictly singular extremal that is not length-minimizing.
3. An Open Mapping Theorem(arXiv)
Abstract : It is proved that any surjective morphism f:Zκ→K onto a locally compact group K is open for every cardinal κ. This answers a question posed by Karl Heinrich Hofmann and the second author.
4. A probabilistic proof of the Open Mapping Theorem for analytic functions(arXiv)
Author : Greg Markowsky
Abstract : The conformal invariance of Brownian motion is used to give a short proof of the Open Mapping Theorem for analytic functions.