| Title:
|
Countable sums and products of Loeb and selective metric spaces (English) |
| Author:
|
Herrlich, Horst |
| Author:
|
Keremedis, Kyriakos |
| Author:
|
Tachtsis, Eleftherios |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
373-384 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces. (English) |
| Keyword:
|
axiom of choice |
| Keyword:
|
weak axioms of choice |
| Keyword:
|
Loeb metric spaces |
| Keyword:
|
selective metric spaces |
| Keyword:
|
countable Tychonoff products of metric spaces |
| Keyword:
|
countable sums of metric spaces |
| MSC:
|
03E25 |
| MSC:
|
54A35 |
| MSC:
|
54D45 |
| MSC:
|
54E50 |
| MSC:
|
54E99 |
| idZBL:
|
Zbl 1121.03063 |
| idMR:
|
MR2176899 |
| . |
| Date available:
|
2009-05-05T16:51:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119531 |
| . |
| Reference:
|
[1] Herrlich H., Strecker G.E.: When is $\Bbb N$ Lindelöf?.Comment. Math. Univ. Carolinae 38 (1998), 553-556. MR 1485075 |
| Reference:
|
[2] Howard P., Rubin J.E.: Consequences of the Axiom of Choice.Amer. Math. Soc., Math. Surveys and Monographs, Vol. 59, Providence (RI), 1998. Zbl 0947.03001, MR 1637107 |
| Reference:
|
[3] Jech T.: The Axiom of Choice.North-Holland, Amsterdam, 1973. Zbl 0259.02052, MR 0396271 |
| Reference:
|
[4] Keremedis K.: The failure of the axiom of choice implies unrest in the theory of Lindelöf metric spaces.Math. Log. Quart. 49 2 (2003), 179-186. Zbl 1016.03051, MR 1961460 |
| Reference:
|
[5] Kelley J.: The Tychonoff product theorem implies the axiom of choice.Fund. Math. 37 (1950), 75-76. Zbl 0039.28202, MR 0039982 |
| Reference:
|
[6] Keremedis K.: Consequences of the failure of the axiom of choice in the theory of Lindelöf metric spaces.Math. Log. Quart. 50 2 (2004), 1-11. Zbl 1041.54022, MR 2037733 |
| Reference:
|
[7] Keremedis K., Tachtsis E.: On Lindelöf metric spaces and weak forms of the axiom of choice.Math. Log. Quart. 46 (2000), 35-44. Zbl 0952.03060, MR 1736648 |
| Reference:
|
[8] Keremedis K., Tachtsis E.: Compact metric spaces and weak forms of the axiom of choice.Math. Log. Quart. 47 (2001), 117-128. Zbl 0968.03057, MR 1808950 |
| Reference:
|
[9] Keremedis K., Tachtsis E.: On Loeb and weakly Loeb Hausdorff spaces.Sci. Math. Jpn. 53 (2001), 247-251. Zbl 0982.54001, MR 1828263 |
| Reference:
|
[10] Keremedis K., Tachtsis E.: Some weak forms of the axiom of choice restricted to the real line.Math. Log. Quart. 47 (2001), 413-422. Zbl 1001.03044, MR 1847457 |
| Reference:
|
[11] Keremedis K., Tachtsis E.: Countable sums and products of metrizable spaces in ZF.Math. Log. Quart. 51 1 (2005), 95-103. Zbl 1059.03048, MR 2099390 |
| Reference:
|
[12] Keremedis K., Tachtsis E.: Topology in the absence of the axiom of choice.Sci. Math. Jpn. 59 2 (2004), 357-406. Zbl 1066.54002, MR 2062202 |
| Reference:
|
[13] Keremedis K., Tachtsis E.: Weak axioms of choice for metric spaces.to appear in Proc. Amer. Math. Soc. Zbl 1090.03021, MR 2163609 |
| Reference:
|
[14] Kunen K.: Set Theory. An Introduction to Independence Proofs.North-Holland, Amsterdam, 1983. Zbl 0534.03026, MR 0756630 |
| Reference:
|
[15] Loeb P.A.: A new proof of the Tychonoff theorem.Amer. Math. Monthly 72 (1965), 711-717. Zbl 0146.18404, MR 0190896 |
| Reference:
|
[16] Tachtsis E.: Disasters in metric topology without choice.Comment. Math. Univ. Carolinae 43 1 (2002), 165-174. Zbl 1072.03030, MR 1903316 |
| Reference:
|
[17] Willard S.: General Topology.Addison-Wesley Publ. Co., Reading, 1970. Zbl 1052.54001, MR 0264581 |
| . |
