Abstract
We introduce the notion of variative seminormal functor F and prove that, for each of these functors and every compact space X, the normality of the space F(X) X implies that the character of X is countable. Thus, we obtain a generalization of the Arkhangel’skiĭ-Kombarov theorem of 1990 on the countability of the character of a compact space which is normal outside the diagonal. Under the assumption of Jensen’s principle, we prove that the above assertion fails for finite nonvariative functors.
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Petrozavodsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 2, pp. 368–376, March–April, 2015.
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Ivanov, A.V. Some generalization of the Arkhangel’skiĭ-Kombarov theorem for seminormal functors. Sib Math J 56, 297–303 (2015). https://doi.org/10.1134/S0037446615020093
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DOI: https://doi.org/10.1134/S0037446615020093