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Transactions of the American Mathematical Society

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

 

 

L'espace des arcs d'une surface


Author: Robert Cauty
Journal: Trans. Amer. Math. Soc. 332 (1992), 193-209
MSC: Primary 57N20; Secondary 54B20, 54F15, 57N05
DOI: https://doi.org/10.1090/S0002-9947-1992-1044960-7
MathSciNet review: 1044960
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Abstract: We prove that, for any surface $ M$, the space of arcs contained in $ M$, with the topology induced by the Hausdorff distance, is homeomorphic to $ M \times {\sum}^\infty $, where $ \sum = \{ ({x_i}) \in {l^2}/\sum\nolimits_{i = 1}^\infty {{{(i{x_i})}^2} < \infty \} } $.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1044960-7
Article copyright: © Copyright 1992 American Mathematical Society