| Title:
|
An independency result in connectification theory (English) |
| Author:
|
Fedeli, Alessandro |
| Author:
|
Le Donne, Attilio |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
331-334 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let $\psi$ be the following statement: ``a perfect $T_3$-space $X$ with no more than $2^{\frak c}$ clopen subsets is connectifiable if and only if no proper nonempty clopen subset of $X$ is feebly compact". In this note we show that neither $\psi$ nor $\neg \psi$ is provable in ZFC. (English) |
| Keyword:
|
connectifiable |
| Keyword:
|
perfect |
| Keyword:
|
feebly compact |
| MSC:
|
03E35 |
| MSC:
|
54A35 |
| MSC:
|
54C25 |
| MSC:
|
54D05 |
| MSC:
|
54D25 |
| idZBL:
|
Zbl 0976.54018 |
| idMR:
|
MR1732654 |
| . |
| Date available:
|
2009-01-08T18:52:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119089 |
| . |
| Reference:
|
[1] Alas O.T., Tkačenko M.G., Tkachuk V.V., Wilson R.G.: Connectifying some spaces.Topology Appl. 71 (1996), 203-215. MR 1397942 |
| Reference:
|
[2] Alas O.T., Tkačenko M.G., Tkachuk V.V., Wilson R.G.: Connectedness and local connectedness of topological groups and extensions.Comment. Math. Univ. Carolinae, to appear. MR 1756549 |
| Reference:
|
[3] Bagley R.W., Connell E.H., McKnight J.D., Jr.: On properties characterizing pseudocompact spaces.Proc. A.M.S. 9 (1958), 500-506. MR 0097043 |
| Reference:
|
[4] van Douwen E.K.: The integers and topology.111-167 Handbook of Set-theoretic Topology (Kunen K. and Vaughan J.E., eds.) Elsevier Science Publishers B.V., North Holland (1984). Zbl 0561.54004, MR 0776622 |
| Reference:
|
[5] Engelking R.: General Topology.Sigma series in Pure Mathematics 6, Heldermann Verlag, Berlin (1989). Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] Fedeli A., Le Donne A.: On locally connected connectifications.Topology Appl. (1998). Zbl 0928.54018 |
| Reference:
|
[7] Fedeli A., Le Donne A.: Connectifications and open components.submitted. Zbl 0953.54023 |
| Reference:
|
[8] Kunen K.: Set Theory.North Holland (1980). Zbl 0443.03021, MR 0597342 |
| Reference:
|
[9] Ostaszewski A.J.: On countably compact, perfectly normal spaces.J. London Math. Soc. (2) 14 (1976), 505-516. Zbl 0348.54014, MR 0438292 |
| Reference:
|
[10] Porter J.R., Woods R.G.: Subspaces of connected spaces.Topology Appl. 68 (1996), 113-131. Zbl 0855.54025, MR 1374077 |
| Reference:
|
[11] Swardson M.A.: Nearly realcompact spaces and $T_2$-connectifiability.358-361 Proceedings of the 8th Prague Topological Symposium (1996). MR 1617114 |
| Reference:
|
[12] Vaughan J.E.: Countably compact and sequentially compact spaces.569-602 Handbook of Set-theoretic Topology (Kunen K. and Vaughan J.E., eds.) Elsevier Science Publishers B.V., North Holland (1984). Zbl 0562.54031, MR 0776631 |
| Reference:
|
[13] Watson S., Wilson R.G.: Embeddings in connected spaces.Houston J. Math. 19 (1993), 3 469-481. Zbl 0837.54012, MR 1242433 |
| Reference:
|
[14] Weiss W.A.R.: Countably compact spaces and Martin's axiom.Canad. J. Math. 30 (1978), 243-249. Zbl 0357.54019, MR 0467673 |
| . |
