The space consisting of uniformly continuous functions on a metric measure space with the $L^p$ norm

Abstract

In this paper, we shall show that the space of real-valued uniformly continuous functions on a metric measure space with the $L^p$ norm is homeomorphic to the subspace consisting of sequences conversing to $0$ in the pseudo interior.

arXiv commentTheorem 1.1 has been revised on the separability of Lp space. (The main result and its argument are not changed.)