A new version of homotopical Hausdorff

Details A new version of homotopical Hausdorff A new version of homotopical Hausdorff

2011-04-05

arxiv.org/abs/1104.0855v1

Mathematics

Geometric Topology

Scientific paper

It is known that shape injectivity implies homotopical Hausdorff. In "On small homotopies of loops" the authors show that the converse does not hold, even if the space is required to be a Peano continuum. This paper gives an alternative definition of homotopical Hausdorff inspired by a new topology on the set of fixed endpoint homotopy classes of paths. This version is equivalent to shape injectivity for Peano spaces.

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