On Products of F-Compact Spaces
- Authors: Ivanov A.V.1
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Affiliations:
- Institute of Applied Mathematical Research
- Issue: Vol 59, No 2 (2018)
- Pages: 270-275
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171755
- DOI: https://doi.org/10.1134/S003744661802009X
- ID: 171755
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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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About the authors
A. V. Ivanov
Institute of Applied Mathematical Research
Author for correspondence.
Email: alvlivanov@krc.karelia.ru
Russian Federation, Petrozavodsk