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Pointed Gromov-Hausdorff Distance between lp-Wedge Sums and Isometric Embeddings of l∞

Abstract

The paper studies lp-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∞ into the Gromov-Hausdorff space of all non-empty metric spaces is proved.

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BibTeX
@misc{abdullaev2026pointed,
  title = {{Pointed Gromov-Hausdorff Distance between $l^p$-Wedge Sums and Isometric Embeddings of $l^\infty$}},
  author = {Emin Abdullaev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12626},
  eprint = {2610.12626},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12626},
}
RIS
TY  - UNPB
TI  - Pointed Gromov-Hausdorff Distance between l^p-Wedge Sums and Isometric Embeddings of l^∞
AU  - Emin Abdullaev
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12626
UR  - https://arxiv.org/abs/2610.12626
AB  - 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^∞ into the Gromov-Hausdorff space of all non-empty metric spaces is proved.
ER  -