QN-spaces, wQN-spaces and covering properties

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• 作者：Lev Bukovský ; ; Jozef Haleš
• 关键词：QN-space ; wQN-space ; Property none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V1K-4M7V9WB-3&_mathId=mml10&_user=10&_cdi=5677&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=5b808448802e740
• 刊名：Topology and its Applications
• 出版年：2007
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：15 February 2007
• 卷：154
• 期：4
• 页码：848-858
• 文件大小：173 K

摘要

The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that 1K-4M7V9WB-3&_mathId=mml1&_user=10&_cdi=5677&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=9e7133fbdc391459c1f41cab1690f871" title="Click to view the MathML source">C_p(X) has the Arkhangel'skiıˇ property (α₁) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, C_p(X) and Arhangel'skiıˇ's α_i-spaces, Topology Appl. 89 (1998) 265–275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of C_p(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S₁(Γ_shr,Γ). Moreover we show that X is a QN-space if and only if C_p(X) has the property (α₀), and for perfectly normal spaces, if and only if X has the covering property (β₃).