Countable sums and products of Loeb and selective metric spaces

Horst Herrlich; Kyriakos Keremedis; Eleftherios Tachtsis

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 2, page 373-384
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Herrlich, Horst, Keremedis, Kyriakos, and Tachtsis, Eleftherios. "Countable sums and products of Loeb and selective metric spaces." Commentationes Mathematicae Universitatis Carolinae 46.2 (2005): 373-384. <http://eudml.org/doc/249526>.

@article{Herrlich2005,
abstract = {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.},
author = {Herrlich, Horst, Keremedis, Kyriakos, Tachtsis, Eleftherios},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {axiom of choice; weak axioms of choice; Loeb metric spaces; selective metric spaces; countable Tychonoff products of metric spaces; countable sums of metric spaces; axiom of choice; weak axioms of choice},
language = {eng},
number = {2},
pages = {373-384},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Countable sums and products of Loeb and selective metric spaces},
url = {http://eudml.org/doc/249526},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Herrlich, Horst
AU - Keremedis, Kyriakos
AU - Tachtsis, Eleftherios
TI - Countable sums and products of Loeb and selective metric spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 2
SP - 373
EP - 384
AB - 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.
LA - eng
KW - axiom of choice; weak axioms of choice; Loeb metric spaces; selective metric spaces; countable Tychonoff products of metric spaces; countable sums of metric spaces; axiom of choice; weak axioms of choice
UR - http://eudml.org/doc/249526
ER -

References

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  1. Herrlich H., Strecker G.E., When is ℕ Lindelöf?, Comment. Math. Univ. Carolinae 38 (1998), 553-556. (1998) MR1485075
  2. Howard P., Rubin J.E., Consequences of the Axiom of Choice, Amer. Math. Soc., Math. Surveys and Monographs, Vol. 59, Providence (RI), 1998. Zbl0947.03001MR1637107
  3. Jech T., The Axiom of Choice, North-Holland, Amsterdam, 1973. Zbl0259.02052MR0396271
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  5. Kelley J., The Tychonoff product theorem implies the axiom of choice, Fund. Math. 37 (1950), 75-76. (1950) Zbl0039.28202MR0039982
  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. (2004) Zbl1041.54022MR2037733
  7. Keremedis K., Tachtsis E., On Lindelöf metric spaces and weak forms of the axiom of choice, Math. Log. Quart. 46 (2000), 35-44. (2000) Zbl0952.03060MR1736648
  8. Keremedis K., Tachtsis E., Compact metric spaces and weak forms of the axiom of choice, Math. Log. Quart. 47 (2001), 117-128. (2001) Zbl0968.03057MR1808950
  9. Keremedis K., Tachtsis E., On Loeb and weakly Loeb Hausdorff spaces, Sci. Math. Jpn. 53 (2001), 247-251. (2001) Zbl0982.54001MR1828263
  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. (2001) Zbl1001.03044MR1847457
  11. Keremedis K., Tachtsis E., Countable sums and products of metrizable spaces in ZF, Math. Log. Quart. 51 1 (2005), 95-103. (2005) Zbl1059.03048MR2099390
  12. Keremedis K., Tachtsis E., Topology in the absence of the axiom of choice, Sci. Math. Jpn. 59 2 (2004), 357-406. (2004) Zbl1066.54002MR2062202
  13. Keremedis K., Tachtsis E., Weak axioms of choice for metric spaces, to appear in Proc. Amer. Math. Soc. Zbl1090.03021MR2163609
  14. Kunen K., Set Theory. An Introduction to Independence Proofs, North-Holland, Amsterdam, 1983. Zbl0534.03026MR0756630
  15. Loeb P.A., A new proof of the Tychonoff theorem, Amer. Math. Monthly 72 (1965), 711-717. (1965) Zbl0146.18404MR0190896
  16. Tachtsis E., Disasters in metric topology without choice, Comment. Math. Univ. Carolinae 43 1 (2002), 165-174. (2002) Zbl1072.03030MR1903316
  17. Willard S., General Topology, Addison-Wesley Publ. Co., Reading, 1970. Zbl1052.54001MR0264581

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