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Perfect κ‐Normality of Product Spaces
Author(s) -
OHTA HARUTO,
SAKAI MASAMI,
TAMANO KENICHI
Publication year - 1993
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1993.tb52530.x
Subject(s) - paracompact space , normal space , mathematics , space (punctuation) , product (mathematics) , normality , product topology , zero (linguistics) , closure (psychology) , combinatorics , mathematical analysis , pure mathematics , topological space , geometry , hausdorff space , computer science , topological vector space , philosophy , economics , market economy , operating system , statistics , linguistics
. A space X is called perfectly K‐normal (respectively, Klebanov) if the closure of every open set (respectively, every union of zero‐sets) in X is a zero‐set. It is proved: The product of infinitely many Lašnev spaces need not be perfectly K‐normal, in particular, S (ω 1 ) 2 χ D ω1 is not perfectly K‐normal; a locally compact, paracompact space Y is Klebanov if and only if X χ Y is perfectly K‐normal for every Lašnev space X ; if X χ Y is perfectly K‐normal for every paracompact s̀‐space X , then Y is perfectly normal. Properties of a Klebanov space are also studied.