I-weight of compact and locally compact LOTS
Commentationes Mathematicae Universitatis Carolinae (2007)
- Volume: 48, Issue: 4, page 677-688
- ISSN: 0010-2628
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topBailey, Brad. "I-weight of compact and locally compact LOTS." Commentationes Mathematicae Universitatis Carolinae 48.4 (2007): 677-688. <http://eudml.org/doc/250229>.
@article{Bailey2007,
abstract = {Ram’ırez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight, Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary and sufficient condition for i-weight to reflect cardinal $\kappa $.},
author = {Bailey, Brad},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {i-weight; reflection; T$_1$-separating weight; LOTS; compact; i-weight; reflection; T-separating weight; LOTS; compact},
language = {eng},
number = {4},
pages = {677-688},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {I-weight of compact and locally compact LOTS},
url = {http://eudml.org/doc/250229},
volume = {48},
year = {2007},
}
TY - JOUR
AU - Bailey, Brad
TI - I-weight of compact and locally compact LOTS
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 4
SP - 677
EP - 688
AB - Ram’ırez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight, Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary and sufficient condition for i-weight to reflect cardinal $\kappa $.
LA - eng
KW - i-weight; reflection; T$_1$-separating weight; LOTS; compact; i-weight; reflection; T-separating weight; LOTS; compact
UR - http://eudml.org/doc/250229
ER -
References
top- Engelking R., General Topology, Helderman, Berlin, 1989. Zbl0684.54001MR1039321
- Hajnal A., Juhász I., Having a small weight is determined by the small subspaces, Proc. Amer. Math. Soc. 79 (1980), 4 657-658. (1980) MR0572322
- Hodel R., Cardinal functions I, in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.1-61. Zbl0559.54003MR0776620
- Hodel R.E., Vaughan J.E., Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47-66. (2000) Zbl0943.54003MR1731704
- Ramírez-Páramo A., A reflection theorem for i-weight, Topology Proc. 28 (2004), 1 277-281. (2004) Zbl1079.54005MR2105463
- Tkachenko M.G., Chains and cardinals, Soviet Math. Dokl. 119 (1978), 382-385. (1978) Zbl0404.54002
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