Intrinsic flat Arzela-Ascoli theorems

摘要

One of the most powerful theorems in metric geometry is the Arzela-Ascoli Theorem which provides a continuous limit for sequences of equicontinuous functions between two compact spaces. This theorem has been extended by Gromov and Grove-Petersen to sequences of functions with varying domains and ranges where the domains and the ranges respectively converge in the Gromov-Hausdorff sense to compact limit spaces. However such a powerful theorem does not hold when the domains and ranges only converge in the intrinsic flat sense due to the possible disappearance of points in the limit.