On monotone paracompactness

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• 作者：Strashimir G. Popvassilev^a ; ^{strash.pop@gmail.com" class="auth_mail} ; John E. Porter^b ; ^{jporter@murraystate.edu" class="auth_mail}
• 关键词：primary ; 54D20 ; 54D70 ; 54F05 ; 54G20 ; secondary ; 54B10 ; 54B25 ; 54E30
• 刊名：Topology and its Applications
• 出版年：15 April, 2014
• 年：2014
• 卷：167
• 期：Complete
• 页码：1-9
• 全文大小：270 K

文摘

Gartside and Moody proved that a space is protometrizable if and only if it has a monotone star-refinement operator on open covers. They called this property monotone paracompactness but noted that it might be better termed monotone full-normality, and posed the problem of characterizing spaces with a monotone locally-finite operator on open covers. Stares studied related monotone properties but left the above problem open. We introduce N枚therianly locally-finite bases, show that protometrizable spaces have such bases, and that spaces with such bases have a monotone locally-finite operator and are monotonically normal. An example of a non-protometrizable LOTS due to Fuller is shown to have a N枚therianly locally-finite base. The product though not hereditarily normal, has a monotone locally-finite operator, while (where M is the Michael line) does not.