Remarks on monotone (weak) Lindelofness
Remarks on monotone (weak) Lindelofness
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DOI：
10.1016/j.topol.2017.04.009
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发表时间：
2017
影响因子：
0.6
通讯作者：
F. Cammaroto and Masami Sakai
中科院分区：
文献类型：
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作者：
M. Bonanzinga;F. Cammaroto and Masami Sakai
利用Erdös-Rado定理，我们证明了：（1）每个单调弱Lindelöf空间满足如下性质：每个由非空开子集组成的基数c+族都有不可数的连通子族;（2）每个单调Lindelöf空间都有强口径（c+，ω 1），特别是单调Lindelöf空间是遗传c-Lindelöf和遗传c-可分的。(1)对Bonanzinga、Cammaroto和Pansera [3]中提出的一个问题作了回答;（2）对Levy和Matveev [15]中提出的问题作了部分回答。还讨论了单调（弱）Lindelöf空间的一些其他性质。例如，我们证明了空间X的Pixley-Roy空间PR（X）是单调Lindelöf当且仅当X是可数的，并且X的每个有限方幂是单调Lindelöf。
Abstract Using Erdös–Rado's theorem, we show that (1) every monotonically weakly Lindelöf space satisfies the property that every family of cardinality c+ consisting of nonempty open subsets has an uncountable linked subfamily;(2) every monotonically Lindelöf space has strong caliber (c+, ω 1), in particular a monotonically Lindelöf space is hereditarily c-Lindelöf and hereditarily c-separable.(1) gives an answer of a question posed in Bonanzinga, Cammaroto and Pansera [3], and (2) gives partial answers of questions posed in Levy and Matveev [15]. Some other properties on monotonically (weakly) Lindelöf spaces are also discussed. For example, we show that the Pixley–Roy space P R (X) of a space X is monotonically Lindelöf if and only if X is countable and every finite power of X is monotonically Lindelöf.