Removability of Uniform Metric Spaces

In this paper, we investigate the removability of uniform metric spaces. Our main result was the following: let X be a rectifiably connected, locally compact, noncomplete and locally annular quasiconvex metric space, and let P be a countable subset of X which satisfies a quasihyperbolic separation condition. Then the space X is uniform if and only if X∖ P is uniform, quantitatively.