Abstract
An F-compactum or a Fedorchuk compactum is a Hausdorff compact space that admits decomposition into a special well-ordered inverse system with fully closed neighboring projections. We prove that the square of Aleksandroff’s “double arrow” space is not an F-compactum of countable spectral height. Using this, we demonstrate the impossibility of representing the Helly space as the inverse limit of a countable system of resolutions with metrizable fibers. This gives a negative answer to a question posed by Watson in 1992.
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References
Ivanov A. V., “Hereditary normality of F-bicompacta,” Math. Notes, vol. 39, no. 4, 332–334 (1986).
Watson S., “The construction of topological spaces,” in: Recent Progress in General Topology, North-Holland, Amsterdam, London, New York, and Tokyo, 1992, 673–762.
Baranova M. A. and Ivanov A. V., “On the spectral height of F-compact spaces,” Sib. Math. J., vol. 54, no. 3, 388–392 (2013).
Gul'ko S. P. and Shulikina M. S., “Locally uniformly convex norms in the spaces of continuous functions on Fedorchuk’s compacta,” in: Abstracts: Aleksandroff’s Reading (Moscow, May 22–26, 2016), Moscow, 2016,17.
Moltó A., Orihuela J., Troyanski S., and Valdivia M., A Nonlinear Transfer Technique for Renorming, Springer-Verlag, Berlin and Heidelberg (2009) (Lect. Notes Math.; vol. 1951).
Fedorchuk V. V., “Fully closed mappings and their applications,” J. Math. Sci. (New York), vol. 136, no. 5, 4201–4292 (2006).
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Original Russian Text Copyright © 2018 Ivanov A.V.
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Ivanov, A.V. On Products of F-Compact Spaces. Sib Math J 59, 270–275 (2018). https://doi.org/10.1134/S003744661802009X
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DOI: https://doi.org/10.1134/S003744661802009X