# Two improvements on Tkačenko's addition theorem

János Gerlits; István Juhász; Zoltán Szentmiklóssy

Commentationes Mathematicae Universitatis Carolinae (2005)

- Volume: 46, Issue: 4, page 705-710
- ISSN: 0010-2628

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topGerlits, 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 -

## References

top- Arhangel'skii A.V., $D$-spaces and covering properties, Topology Appl. 146-147 (2005), 437-449. (2005) Zbl1063.54013MR2107163
- Gerlits J., Juhász I., On left-separated compact spaces, Comment. Math. Univ. Carolinae 19 (1978), 53-62. (1978) MR0487982
- Gruenhage G., A note on $D$-spaces, preprint. Zbl1101.54029MR2238727
- Juhász I., Shelah S., $\pi \left(X\right)=\delta \left(X\right)$ for compact $X$, Topology Appl. 32 (1989), 289-294. (1989) Zbl0688.54002MR1007107
- Simon P., Left-separated spaces: a comment to a paper of M.G. Tkačenko, Comment. Math. Univ. Carolinae 20 (1979), 597-603. (1979) MR0550459
- Tkačenko M.G., O bikompaktah predstavimyh v vide obedidenia schetnogo chisla levych podprostranstv I, II, Comment. Math. Univ. Carolinae 20 (1979), 361-379 and 381-395. (1979) MR0539565
- van Douwen E., Pfeffer W.F., Some properties of the Sorgenfrey-line and related spaces, Pacific J. Math. 81 (1979), 371-377. (1979) Zbl0409.54011MR0547605
- Weston J.H., Shilleto J., Cardinalities of dense sets, Gen. Topology Appl. 6 (1976), 227-240. (1976) Zbl0321.54003MR0442875

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