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In the first of these lectures (http://www.mpim-bonn.mpg.de/node/4436) given by M. Freedman he says that there exists (compact metric) spaces $X$ and $Y$ such that $X\times S^{1}$ is homeomorphic to $Y\times S^{1}$ but $X\times \mathbb{R}$ is not homeomorphic to $Y\times\mathbb{R}$.

Does anyone know an example of such spaces?

Dario
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  • This question has better chance to be answered at mathoverflow. – Moishe Kohan Jun 13 '14 at 21:57
  • Thank you for the suggestion! I'll put it also there! – Dario Jun 13 '14 at 21:58
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    Also check references in http://www.morfismos.cinvestav.mx/Portals/0/SiteDocs/Articulos/Volumen2/No1/Santillan/santillan.pdf: Maybe one of them will answer your question. – Moishe Kohan Jun 13 '14 at 22:03
  • On Mathoverflow I was suggested to look at: http://math.stackexchange.com/questions/396608/does-x-times-s1-cong-y-times-s1-imply-that-x-times-mathbb-r-cong-y-times-ma/410699#410699 (It is indeed the same question, and even the source was the same) – Dario Jun 14 '14 at 10:34
  • Good. This means that your question can now be closed as a duplicate. – Moishe Kohan Jun 15 '14 at 16:24

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