Summary
In this paper we prove that, ifS ×R n is homeomorphic toR n + 1, thenS is homeomorphic toR.
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References
Bing, R. H.,The Cartesian product of a certain nonmanifold and line is E 4. Ann of Math.70 (1959).
Borsuk, K.,Concerning the Cartesian division by manifolds. Bull. Acad. Polon. Sci.1 (1953), 91–94.
Borsuk, K.,On the decomposition of a locally connected compactum into Cartesian product of a curve and a manifold. Fund. Math.40 (1953), 140–159.
Patkowska, H.,On the uniqueness of the decomposition of finite-dimensional ANR-s into Cartesian products of at most 1-dimensional spaces. Fund. Math.58 (1966), 89–110.
Zdun, M. C.,Problem P293. Aequationes Math.48 (1994), 114.
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Tabor, J. On the division by Rn . Aeq. Math. 49, 300–303 (1995). https://doi.org/10.1007/BF01827947
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DOI: https://doi.org/10.1007/BF01827947