Standard

On the coincidence of the canonical embeddings of a metric space into a Banach space. / Zatitskiy, P. B.

In: Journal of Mathematical Sciences, Vol. 158, No. 6, 01.05.2009, p. 853-857.

Research output: Contribution to journal › Article › peer-review

Harvard

Zatitskiy, PB 2009, 'On the coincidence of the canonical embeddings of a metric space into a Banach space', Journal of Mathematical Sciences, vol. 158, no. 6, pp. 853-857. https://doi.org/10.1007/s10958-009-9422-2

APA

Zatitskiy, P. B. (2009). On the coincidence of the canonical embeddings of a metric space into a Banach space. Journal of Mathematical Sciences, 158(6), 853-857. https://doi.org/10.1007/s10958-009-9422-2

Vancouver

Zatitskiy PB. On the coincidence of the canonical embeddings of a metric space into a Banach space. Journal of Mathematical Sciences. 2009 May 1;158(6):853-857. https://doi.org/10.1007/s10958-009-9422-2

Author

Zatitskiy, P. B. / On the coincidence of the canonical embeddings of a metric space into a Banach space. In: Journal of Mathematical Sciences. 2009 ; Vol. 158, No. 6. pp. 853-857.

BibTeX

@article{39dc3823d2b64a92a80e6eb1a9b6a85c,
title = "On the coincidence of the canonical embeddings of a metric space into a Banach space",
abstract = "Recall the two classical canonical isometric embeddings of a finite metric space X into a Banach space. That is, the Hausdorff-Kuratowsky embedding x∈→∈ρ(x, ·) into the space of continuous functions on X with the max-norm, and the Kantorovich-Rubinshtein embedding x∈→∈δ x (where δ x , is the δ-measure concentrated at x) with the transportation norm. We prove that these embeddings are not equivalent if |X|∈>∈4.",
author = "Zatitskiy, {P. B.}",
year = "2009",
month = may,
day = "1",
doi = "10.1007/s10958-009-9422-2",
language = "English",
volume = "158",
pages = "853--857",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - On the coincidence of the canonical embeddings of a metric space into a Banach space

AU - Zatitskiy, P. B.

PY - 2009/5/1

Y1 - 2009/5/1

N2 - Recall the two classical canonical isometric embeddings of a finite metric space X into a Banach space. That is, the Hausdorff-Kuratowsky embedding x∈→∈ρ(x, ·) into the space of continuous functions on X with the max-norm, and the Kantorovich-Rubinshtein embedding x∈→∈δ x (where δ x , is the δ-measure concentrated at x) with the transportation norm. We prove that these embeddings are not equivalent if |X|∈>∈4.

AB - Recall the two classical canonical isometric embeddings of a finite metric space X into a Banach space. That is, the Hausdorff-Kuratowsky embedding x∈→∈ρ(x, ·) into the space of continuous functions on X with the max-norm, and the Kantorovich-Rubinshtein embedding x∈→∈δ x (where δ x , is the δ-measure concentrated at x) with the transportation norm. We prove that these embeddings are not equivalent if |X|∈>∈4.

UR - http://www.scopus.com/inward/record.url?scp=67349243418&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9422-2

DO - 10.1007/s10958-009-9422-2

M3 - Article

AN - SCOPUS:67349243418

VL - 158

SP - 853

EP - 857

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 36193894