Abstract
We establish that condition (Γ) on brick decomposition is indecomposable. This answers K. Borsuk’s question [1]. We prove that there exist metric spaces X and Y and a point (a, b) ∈ X × Y such that (a, b) is an r-point of the product X × Y; moreover, a is not an r-point of X. This answers A. Kosinski’s question [2].
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References
Borsuk K., Theory of Retracts [Russian translation], Mir, Moscow (1971).
Kosinski A., “On manifolds and r-spaces,” Fund. Math., 42, 111–124 (1955).
Chapman T. A., Lectures on Hilbert Cube Manifolds [Russian translation], Mir, Moscow (1981).
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Original Russian Text Copyright © 2007 Chernikov P. V.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 236–237, January–February, 2007.
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Chernikov, P.V. On two questions of the theory of retracts. Sib Math J 48, 189–190 (2007). https://doi.org/10.1007/s11202-007-0020-6
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DOI: https://doi.org/10.1007/s11202-007-0020-6