Pointed Gromov-Hausdorff Distance between $l^p$-Wedge Sums and Isometric Embeddings of $l^\infty$

Abstract

The paper studies $l^p$-wedge sums of metric spaces and provides a two-sided estimate for the pointed Gromov-Hausdorff distance between them. Using an upper bound for the Gromov-Hausdorff distance, the existence of an isometric embedding of $l^\infty$ into the Gromov-Hausdorff space of all non-empty metric spaces is proved.