Rigid subsets in Euclidean and Hilbert spaces
1975 ◽
Vol 20
(1)
◽
pp. 66-72
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Keyword(s):
AbstractA subset Y of a metric space (X, p) is called rigid if all the distances p(y1, y2) between points y1, y2 ∈ Y in Y are mutually different. The main purpose of this paper is to prove the existence of dense rigid subsets of cardinality c in Euclidean spaces En and in the separable Hilbert space l2. Some applications to abstract point set geometries are given and the connection with the theory of dimension is discussed.
2015 ◽
Vol 93
(1)
◽
pp. 146-151
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Keyword(s):
2007 ◽
Vol 10
(02)
◽
pp. 261-276
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2009 ◽
Vol 01
(01)
◽
pp. 87-100
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2012 ◽
Vol 04
(02)
◽
pp. 237-253
◽
2002 ◽
Vol 32
(3)
◽
pp. 177-182
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2014 ◽
Vol 17
(02)
◽
pp. 1450013
◽
2021 ◽
Vol 24
(01)
◽
pp. 2150009
2021 ◽