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 Mat. Zametki, 2015, Volume 98, Issue 2, Pages 221–229 (Mi mz10237)

An Example of a Compact Space of Uncountable Character for Which the Space $\exp_n(X)\setminus X$ is Normal

A. V. Ivanov

Petrozavodsk State University

Abstract: 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.

DOI: https://doi.org/10.4213/mzm10237

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English version:
Mathematical Notes, 2015, 98:2, 251–257

Bibliographic databases:

UDC: 515.12
Revised: 09.08.2013

Citation: A. V. Ivanov, “An Example of a Compact Space of Uncountable Character for Which the Space $\exp_n(X)\setminus X$ is Normal”, Mat. Zametki, 98:2 (2015), 221–229; Math. Notes, 98:2 (2015), 251–257

Citation in format AMSBIB
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