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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 279, Pages 89–110 (Mi znsl1455)  
Metric axioms of Euclidean space

A. A. Ivanov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (209 kB)
Abstract: A version of axioms of Euclidean space based on the sole intain notion, namely on the notion of distance, is considered. The notions of straight line and plane are introduced in the terms of distance. Thus, Euclidean space is considered here as a metric space with metric satisfying the corresponding axioms.
Received: 09.01.2001
English version:
Journal of Mathematical Sciences (New York), 2004, Volume 119, Issue 1, Pages 45–54
DOI: https://doi.org/10.1023/B:JOTH.0000008740.64892.31
Bibliographic databases:
UDC: 515.124+514.12.01
Language: Russian
Citation: A. A. Ivanov, “Metric axioms of Euclidean space”, Geometry and topology. Part 6, Zap. Nauchn. Sem. POMI, 279, POMI, St. Petersburg, 2001, 89–110; J. Math. Sci. (N. Y.), 119:1 (2004), 45–54
Citation in format AMSBIB
\Bibitem{Iva01}
\by A.~A.~Ivanov
\paper Metric axioms of Euclidean space
\inbook Geometry and topology. Part~6
\serial Zap. Nauchn. Sem. POMI
\yr 2001
\vol 279
\pages 89--110
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1455}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1846074}
\zmath{https://zbmath.org/?q=an:1076.51507}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2004
\vol 119
\issue 1
\pages 45--54
\crossref{https://doi.org/10.1023/B:JOTH.0000008740.64892.31}
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