Two improvements on Tkačenko's addition theorem

Gerlits, János, Juhász, István, and Szentmiklóssy, Zoltán. "Two improvements on Tkačenko's addition theorem." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 705-710. <http://eudml.org/doc/249552>.

@article{Gerlits2005,
abstract = {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 $N(\mathbb \{R\})$ = $\operatorname\{cov\} (\mathcal \{M\})$ 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.},
author = {Gerlits, János, Juhász, István, Szentmiklóssy, Zoltán},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$D$-space; left separated; compact; countably compact; scattered space; Novák number; -space; left separated; compact; countably compact; scattered space; Novák number},
language = {eng},
number = {4},
pages = {705-710},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Two improvements on Tkačenko's addition theorem},
url = {http://eudml.org/doc/249552},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Gerlits, János
AU - Juhász, István
AU - Szentmiklóssy, Zoltán
TI - Two improvements on Tkačenko's addition theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 705
EP - 710
AB - 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 $N(\mathbb {R})$ = $\operatorname{cov} (\mathcal {M})$ 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.
LA - eng
KW - $D$-space; left separated; compact; countably compact; scattered space; Novák number; -space; left separated; compact; countably compact; scattered space; Novák number
UR - http://eudml.org/doc/249552
ER -