Александровские чтения-2016 | 22-26 мая 2016
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 Участник: Якивчик Андрей Николаевич
 Имя: Якивчик Андрей НиколаевичНазвание: 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.

© 2016 Механико-математический факультет МГУ им. М.В. Ломоносова