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Zbl 1121.54041
Gerlits, J.; Juhász, I.; Szentmiklóssy, Z.
Two improvements on Tkačenko's addition theorem. (English)
[J] Commentat. Math. Univ. Carol. 46, No. 4, 705-710 (2005). ISSN 0010-2628

Summary: 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 $N(\Bbb R)$ = $\text {cov}(\Cal M)$ left-separated subspaces then it is scattered. Both (A) and (B) improve results of {\it M.\,G.\,Tkačenko} from 1979; (A) also answers a question that was raised by {\it A.\,V.\,Arhangel'skii} and improves a result of {\it G.\,Gruenhage}.

MSC 2000:: *54D55 Sequential spaces
54G12 Scattered spaces
54A25 Cardinality properties of topological spaces

Keywords: $D$-space; left separated; compact; countably compact; scattered space; Novák number

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