On fully closed mappings of Fedorchuk compacta
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 50 (2017), pp. 5-8
Cet article a éte moissonné depuis la source Math-Net.Ru
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.
@article{VTGU_2017_50_a0,
author = {S. P. Gul'ko and A. V. Ivanov},
title = {On fully closed mappings of {Fedorchuk} compacta},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {5--8},
year = {2017},
number = {50},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2017_50_a0/}
}
S. P. Gul'ko; A. V. Ivanov. On fully closed mappings of Fedorchuk compacta. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 50 (2017), pp. 5-8. http://geodesic.mathdoc.fr/item/VTGU_2017_50_a0/