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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ k$-congruence orders for $ E\sb{k}$


Author: Grattan P. Murphy
Journal: Trans. Amer. Math. Soc. 177 (1973), 405-412
MSC: Primary 52A50
DOI: https://doi.org/10.1090/S0002-9947-1973-0319059-3
MathSciNet review: 0319059
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Abstract: This paper generalizes the notion of congruence order for metric spaces to k-metric (k-dimensional metric) spaces. The k-congruence order of $ {E_k}$ with respect to the class of oriented semi k-metric spaces is determined. An example shows that this result is sharp.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0319059-3
Keywords: Congruence order, k-dimensional metrics, congruent imbedding in Euclidean space
Article copyright: © Copyright 1973 American Mathematical Society