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Sibirsk. Mat. Zh., 2018, Volume 59, Number 2, Pages 345–352 (Mi smj2976)  

This article is cited in 1 scientific paper (total in 1 paper)

On products of $F$-compact spaces

A. V. Ivanov

Institute of Applied Mathematical Research, Petrozavodsk, Russia

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.

Keywords: $F$-compactum, fully closed mapping, Helly space, resolution.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-51-18051
The author was supported by the Russian Foundation for Basic Research (Grant 17-51-18051).


DOI: https://doi.org/10.17377/smzh.2018.59.209

Full text: PDF file (288 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:2, 270–275

Bibliographic databases:

UDC: 515.12
Received: 09.08.2017

Citation: A. V. Ivanov, “On products of $F$-compact spaces”, Sibirsk. Mat. Zh., 59:2 (2018), 345–352; Siberian Math. J., 59:2 (2018), 270–275

Citation in format AMSBIB
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\pages 270--275
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ivanov A.V., “The Class of Fedorchuk Compact Spaces Is Anti-Multiplicative”, Topology Appl., 235 (2018), 485–491  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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