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give a reference
A good reference is: Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry , Graduate Studies in Mathematics, Vol. 33, American Mathematical Society, 2001.
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Key takeaways
- A good reference is: Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry , Graduate Studies in Mathematics, Vol.
- 33, American Mathematical Society, 2001.
- This is a standard metric geometry reference; the available evidence lists the authors, publisher, series, volume, year, and ISBN information for the book [8].
- It is also recommended as a valuable source for concepts in metric geometry in notes on the Gromov–Hausdorff distance [7].
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openai.comCreate a landscape editorial hero image for this Studio Global article: give a reference. Article summary: A good reference is: Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry , Graduate Studies in Mathematics, Vol.. Topic tags: deepresearch, general web, code, google, education. Reference image context from search candidates: Reference image 1: visual subject "Les utilisateurs de lecteurs d'écran peuvent cliquer sur ce lien pour activer le mode d'accessibilité. Celui-ci propose les mêmes fonctionnalités principales, mais il est optimisé" source context "A Course in Metric Geometry - Dmitri Burago, I︠U︡riĭ Dmitrievich Burago, Sergeĭ Ivanov - Google Livres" Reference image 2: visual subject "A Course in Metric Geometry. Front Cover. Dmitri Burago, I︠U︡riĭ Dmitrievich Burago, Sergeĭ Ivanov. American Mathematical Soc., 2001 - Mathematics - 415 pages." source conte
A good reference is:
Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, Vol. 33, American Mathematical Society, 2001.
This is a standard metric-geometry reference; the available evidence lists the authors, publisher, series, volume, year, and ISBN information for the book . It is also recommended as a valuable source for concepts in metric geometry in notes on the Gromov–Hausdorff distance .
BibTeX
@book{burago2001course,
title = {A Course in Metric Geometry},
author = {Burago, Dmitri and Burago, Yuri and Ivanov, Sergei},
series = {Graduate Studies in Mathematics},
volume = {33},
publisher = {American Mathematical Society},
year = {2001}
}
Sentence you can use
The Hausdorff distance is a metric on the collection of nonempty compact
subsets of a metric space, and hence satisfies the triangle inequality
\cite{burago2001course}.
If you want a direct proof reference
For a direct proof of the triangle inequality for the Hausdorff metric, the available evidence includes course notes that explicitly state “Now we prove the triangle inequality” for the Hausdorff metric on closed bounded subsets of (\mathbb{R}^n) . For a paper, however, I would cite the Burago--Burago--Ivanov book rather than homework notes.
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What is the short answer to "give a reference"?
A good reference is: Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry , Graduate Studies in Mathematics, Vol.
What are the key points to validate first?
A good reference is: Dmitri Burago, Yuri Burago, and Sergei Ivanov, A Course in Metric Geometry , Graduate Studies in Mathematics, Vol. 33, American Mathematical Society, 2001.
What should I do next in practice?
This is a standard metric geometry reference; the available evidence lists the authors, publisher, series, volume, year, and ISBN information for the book [8].