An Example of a Compact Space of Uncountable Character for Which the Space $\exp_n(X)\setminus X$ is Normal
Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 221-229
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Under Jensen's axiom, a compact space $X$ of uncountable character such that the space $\exp_n(X)\setminus X$ is normal for each $n$ is constructed. Thereby, it is proved that the Arkhangelskii–Kombarov theorem on the countability of the character of a compact space whose square is normal outside the diagonal cannot be “naïvely” carried over to normal functors of finite degree.
Keywords:
Katětov's theorem, square of a compact space, first-countable compact space, functor $\exp_n$, Jensen's axiom, normal functor.
@article{MZM_2015_98_2_a6,
author = {A. V. Ivanov},
title = {An {Example} of a {Compact} {Space} of {Uncountable} {Character} for {Which} the {Space} $\exp_n(X)\setminus X$ is {Normal}},
journal = {Matemati\v{c}eskie zametki},
pages = {221--229},
publisher = {mathdoc},
volume = {98},
number = {2},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a6/}
}
TY - JOUR AU - A. V. Ivanov TI - An Example of a Compact Space of Uncountable Character for Which the Space $\exp_n(X)\setminus X$ is Normal JO - Matematičeskie zametki PY - 2015 SP - 221 EP - 229 VL - 98 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a6/ LA - ru ID - MZM_2015_98_2_a6 ER -
A. V. Ivanov. An Example of a Compact Space of Uncountable Character for Which the Space $\exp_n(X)\setminus X$ is Normal. Matematičeskie zametki, Tome 98 (2015) no. 2, pp. 221-229. http://geodesic.mathdoc.fr/item/MZM_2015_98_2_a6/