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Two improvements on Tkačenko's addition theorem

János Gerlits, István Juhász, Zoltán Szentmiklóssy (2005)

Commentationes Mathematicae Universitatis Carolinae

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 T 2 space is the union of fewer than N ( ) = cov ( ) left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkačenko from 1979; (A) also answers a question that was raised by Arhangel’skiǐ and improves a result of Gruenhage.

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