К вопросу о наследственной нормальности пространств вида $\mathcal{F}(x)$
Problemy analiza, no. 16 (2009), pp. 48-54
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Ivanov and Kashuba [1] constructed an example assuming the Continuum Hypothesis. There exists a nonmetrizable compact space $X$, such that the following conditions hold: 1) for any natural number $n$ the compact space $X^{n}$ is hereditarily separable; 2) for any natural number $n$ the space $X^{n}\setminus \Delta_{n}$ is hereditarily normal; 3) for any functor $\mathcal{F}$ preserving weight and one-to-one points the space $\mathcal{F}_{k}(X)$ is hereditarily normal ($k$ is the second element of the degree spectrum $sp(\mathcal{F}))$.
@article{PA_2009_16_a3,
author = {E. V. Kashuba},
title = {{\CYRK} {\cyrv}{\cyro}{\cyrp}{\cyrr}{\cyro}{\cyrs}{\cyru} {\cyro} {\cyrn}{\cyra}{\cyrs}{\cyrl}{\cyre}{\cyrd}{\cyrs}{\cyrt}{\cyrv}{\cyre}{\cyrn}{\cyrn}{\cyro}{\cyrishrt} {\cyrn}{\cyro}{\cyrr}{\cyrm}{\cyra}{\cyrl}{\cyrsftsn}{\cyrn}{\cyro}{\cyrs}{\cyrt}{\cyri} {\cyrp}{\cyrr}{\cyro}{\cyrs}{\cyrt}{\cyrr}{\cyra}{\cyrn}{\cyrs}{\cyrt}{\cyrv} {\cyrv}{\cyri}{\cyrd}{\cyra} $\mathcal{F}(x)$},
journal = {Problemy analiza},
pages = {48--54},
year = {2009},
number = {16},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/PA_2009_16_a3/}
}
E. V. Kashuba. К вопросу о наследственной нормальности пространств вида $\mathcal{F}(x)$. Problemy analiza, no. 16 (2009), pp. 48-54. http://geodesic.mathdoc.fr/item/PA_2009_16_a3/