Two improvements on Tkaÿcenko's addition theorem
Two improvements on Tkaÿcenko's addition theorem
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发表时间：
2005
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通讯作者：
J. Gerlits;I. Juhász;Z. Szentmiklóssy
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作者：
J. Gerlits;I. Juhász;Z. Szentmiklóssy
我们证明了：(A)如果一个可数紧空间是可数多个D子空间的并，则它是紧的；(B)如果一个紧T2空间是少于N(R)=cov(M)个左分离子空间的并，则它是离散的。(A)和(B)都改进了1979年Tkaycenko的结果；(A)还回答了Arangel‘skyi提出的一个问题，改进了Gruenage的一个结果。
We prove that (A) if a countably compact space is the union of countably many D subspaces then it is compact; (B) if a compact T2 space is the union of fewer than N(R) = cov(M) left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkaycenko from 1979; (A) also answers a question that was raised by Arhangel'skiyi and improves a result of Gruenhage.