Universal Space
المؤلف:
Fréchet, M.
المصدر:
"Les dimensions d,un ensemble abstrait." Math. Ann. 68
الجزء والصفحة:
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7-8-2021
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Universal Space
A topological space that contains a homeomorphic image of every topological space of a certain class.
A metric space 
is said to be universal for a family of metric spaces 
if any space from 
is isometrically embeddable in 
. Fréchet (1910) proved that 
, the space of all bounded sequences of real numbers endowed with a supremum norm, is a universal space for the family 
of all separable metric spaces. Holsztynski (1978) proved that there exists a metric 
on 
, inducing the usual topology, such that every finite metric space embeds in 
(Ovchinnikov 2000).
REFERENCES:
Fréchet, M. "Les dimensions d'un ensemble abstrait." Math. Ann. 68, 145-168, 1910.
Holsztynski, W. "
as a Universal Metric Space." Not. Amer. Math. Soc. 25, A-367, 1978.
Ovchinnikov, S. "Universal Metric Spaces According to W. Holsztynski." 13 Apr 2000. https://arxiv.org/abs/math.GN/0004091.
Urysohn, P. S. "Sur un espace métrique universel." Bull. de Sciences Math. 5, 1-38, 1927.
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