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Имя: Якивчик Андрей Николаевич Название: On generalized normality and semiregularization topology
Город, страна: Москва, Россия
Организация: Московский государственный университет им. М.В.Ломоносова
Абстракт: A topological space $X$ is \emph{nearly normal} (Mukherjee--Debray 1998, 2005) if any two its disjoint subsets,
of which one is regular closed and the other is $\delta$-closed (i.e., complementary
to a set open in the semiregularization topology on $X$),
have disjoint open neighborhoods. Furthermore, \emph{semi near normality} (Mukherjee--Mandal 2014) of $X$
means separation by open neighborhoods of any two disjoint subsets in $X$, of which
one is arbitrary closed and the other is $\delta$-closed. Using well known plank methods,
we show that a nearly normal Tychonoff space (even possessing many pleasant properties)
may fail to be semi nearly normal. We also discuss relations between several other
generalized normality properties such as almost normality, $\delta$-normality etc.
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