Geodesic
On the Topologies of R∞
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 47-51

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Let R∞ be the set of all the finite sequences of real numbers. The author shows that there are uncountably many distinct topologies on the set R∞, each of which coincides with the usual topology when restricted to an Rn. However, under each of these topologies, R∞ is always of the same homotopy type. A generalization to some other spaces is mentioned. 
Ho, Chung-Wu. On the Topologies of R∞. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 47-51. doi: 10.4153/CMB-1981-007-6
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     title = {On the {Topologies} of {R\ensuremath{\infty}}},
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     doi = {10.4153/CMB-1981-007-6},
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