Abstract
In this paper two Arzela-Ascoli Theorems are proven: one for uniformly Lip- schitz functions whose domains are converging in the intrinsic flat sense, and one for se- quences of uniformly local isometries between spaces which are converging in the intrinsic flat sense. A basic Bolzano-Weierstrass Theorem is proven fo r sequences of points in such sequences of spaces. In addition it is proven that when a sequence of manifolds has a pre- compact intrinsic flat limit then the metric completion of th e limit is the Gromov-Hausdorff limit of regions within those manifolds. Open problems with suggested applications are provided throughout the paper.
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