Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2017, Number 50, Pages 5–8
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,
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.
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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
\by S.~P.~Gul'ko, A.~V.~Ivanov
\paper On fully closed mappings of Fedorchuk compacta
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
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