A study of monotonically normal spaces
نویسندگان
چکیده
منابع مشابه
Kat Etov's Lemma and Monotonically Normal Spaces
An interpolation lemma due to Kat etov is simpliied in order to make it more general and easier to use. Several results are established to illustrate applications of this lemma, including a characterization of monotonically normal spaces and a topology-free insertion theorem. We also prove that a topological space has an order-preserving insertion if and only if it is dominated by a collection ...
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For a compact monotonically normal space X we prove: (1) X has a dense set of points with a well-ordered neighborhood base (and so X is co-absolute with a compact orderable space); (2) each point of X has a well-ordered neighborhood πbase (answering a question of Arhangel’skii); (3) X is hereditarily paracompact iff X has countable tightness. In the process we introduce weak-tightness, a notion...
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We answer questions of Bennett, Lutzer, and Matveev by showing that any monotonically compact LOTS is metrizable, and any first-countable Lindelöf GO-space is monotoncically Lindelöf. We also show that any compact monotonically Lindelöf space is first-countable, and is metrizable if scattered, and that separable monotonically compact spaces are metrizable.
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Article history: Received 17 July 2008 Received in revised form 6 October 2009 MSC: primary 54D20 secondary 54E30, 54E35, 54F05
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0324644-4