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Comparing chains in a Banach space

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Abstract

We prove that in a Banach space with the metric approximation property the flat chains defined by De Pauw and Hardt (Am J Math 134:1–69, 2012) coincide with those of Adams (J Geom Anal 18:1–28, 2008).

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Notes

  1.  For brevity we say \({{\mathscr {H}}}^m\) rectifiable instead of countably \({{\mathscr {H}}}^m\)rectifiable.

  2. At the cost of additional constants, MAP can be relaxed to the bounded approximation property BAP; see [9, Definition 1.e.11].

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  1. Department of Mathematics, University of California, Davis, CA, 95616, USA

    W. F. Pfeffer

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  1. W. F. Pfeffer
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Correspondence to W. F. Pfeffer.

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Pfeffer, W.F. Comparing chains in a Banach space. Ricerche mat 69, 1–11 (2020). https://doi.org/10.1007/s11587-019-00445-z

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  • DOI: https://doi.org/10.1007/s11587-019-00445-z

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