Character and tightness of hyperspaces with the Fell topology
Character and tightness of hyperspaces with the Fell topology
复制标题
Fell 拓扑超空间的特征和紧密性
DOI：
10.1016/s0166-8641(97)00092-8
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发表时间：
1998
影响因子：
0.6
通讯作者：
Ji
中科院分区：
文献类型：
--
作者：
Ji
对于Hausdorff空间X，我们用2X表示X的所有闭子集的集合。Fell拓扑τfon 2X有所有形式为V−= {F <$2X：F <$V <$$>}的集合作为子基，其中V是X的开子集，而形式为（Kc）+= {F <$2X：F <$K =<$}的集合作为子基，其中K是X的紧子集。本文证明了max{dc（X），klo（X），t（X）} ≠ t（τ 2X，τF τ）τ max{dc（X），klo（X），χ（X）}和χ（x ~ 2X，τF_∞）= max{dc（X），kko（X），χ（X）}，其中t（X）和χ（X）分别表示X的紧度和特征，dc（X）是使X的每个闭子集的密度小于或等于τ的最小基数τ; klo（X）和kko（X）是与X的所有紧子集族有关的两个基数不变量。对于局部紧空间X，我们还得到了τ 2X，τF <$的紧性与τ 2X，τF <$的特征是一致的.我们构造一个空间Y，使得t（τ 2 Y，τF）<$max{dc（Y），klo（Y），χ（Y）}。我们还回答了Beer（1993）的一个问题.
For a Hausdorff space X, we denote by 2Xthe collection of all closed subsets of X. The Fell topology τfon 2Xhas as a subbase all sets of the form V−= {Fϵ 2X: F ∩ V ≠ Ø}, where V is an open subset of X and of the form (Kc)+= {Fϵ 2X: F ∩ K = Ø}, where K is a compact subset of X. In this paper we prove that max{dc(X), klo(X), t(X)} ⩽ t(〈2X, τF〉) ⩽ max{dc(X), klo(X), χ(X)} andχ(〈2X, τF〉) = max{dc(X), kko(X), χ(X)}, where t(X) and χ(X) denote the tightness and character of X, respectively, dc(X) is the smallest cardinal number τ such that the density of every closed subset of X is less than or equal to τ; and klo(X) and kko(X) are two cardinal invariants related to the family of all compact subsets of X. We also obtain that for a locally compact space X the tightness of 〈2X, τF〉 and the character of 〈2X, τF〉 coincide. We construct a space Y such that t(〈2Y, τF〉) ≠ max{dc(Y), klo(Y), χ(Y)}. We also give an answer to a question of Beer (1993).