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Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2017, Number 50, Pages 5–8 (Mi vtgu614)  

MATHEMATICS

On fully closed mappings of Fedorchuk compacta

S. P. Gul'koa, A. V. Ivanovb

a Tomsk State University, Tomsk, Russian Federation
b Institute of Applied Mathematics of Karelian Scientific Center of Russian Academy of Sciences, Petrozavodsk, Russian Federation

Abstract: An $F$-compactum or a Fedorchuk compactum is a compact Hausdorff topological space that admits a decomposition into a special fully ordered inverse spectrum with fully closed neighboring projections. $F$-compacta of spectral height $3$ are exactly nonmetrizable compacta that admit a fully closed mapping onto a metric compactum with metrizable fibers.
In this paper, it is proved that such a fully closed mapping for an $F$-compactum $X$ of spectral height $3$ is defined almost uniquely. Namely, nontrivial fibers of any two fully closed mapping of $X$ into metric compacts with metrizable inverse images of points coincide everywhere, with a possible exception of a countable family of elements.
Examples of $F$-compacta of spectral height $3$ are, for example, Aleksandrov’s "two arrows" and the lexicographic square of the segment. It follows from the main result of this paper that almost all non-trivial layers of any admissible fully closed mapping are colons that are glued together under the standard projection of $D$ onto the segment. Similarly, almost all nontrivial fibers of any admissible fully closed mapping necessarily coincide with the "vertical segments" of the lexicographic square.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-51-18051_Болг_а


DOI: https://doi.org/10.17223/19988621/50/1

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Bibliographic databases:

UDC: 515.12
Received: 20.11.2017

Citation: S. P. Gul'ko, A. V. Ivanov, “On fully closed mappings of Fedorchuk compacta”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2017, no. 50, 5–8

Citation in format AMSBIB
\Bibitem{GulIva17}
\by S.~P.~Gul'ko, A.~V.~Ivanov
\paper On fully closed mappings of Fedorchuk compacta
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2017
\issue 50
\pages 5--8
\mathnet{http://mi.mathnet.ru/vtgu614}
\crossref{https://doi.org/10.17223/19988621/50/1}
\elib{http://elibrary.ru/item.asp?id=30778967}


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  • Вестник Томского государственного университета. Математика и механика
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