# Article

 Title: I-weight of compact and locally compact LOTS  (English) Author: Bailey, Brad Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 48 Issue: 4 Year: 2007 Pages: 677-688 . Category: math . Summary: Ram'{\i}rez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [{\it A reflection theorem for i-weight\/}, Topology Proc. {\bf 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 $\kappa$. Keyword: i-weight Keyword: reflection Keyword: T$_1$-separating weight Keyword: LOTS Keyword: compact MSC: 54A05 MSC: 54A25 MSC: 54F05 idZBL: Zbl 1199.54029 idMR: MR2375168 . Date available: 2009-05-05T17:05:38Z Last updated: 2012-05-01 Stable URL: http://hdl.handle.net/10338.dmlcz/119690 . Reference: [1] Engelking R.: General Topology.Helderman, Berlin, 1989. Zbl 0684.54001, MR 1039321 Reference: [2] Hajnal A., Juhász I.: Having a small weight is determined by the small subspaces.Proc. Amer. Math. Soc. 79 (1980), 4 657-658. MR 0572322 Reference: [3] Hodel R.: Cardinal functions I.in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.1-61. Zbl 0559.54003, MR 0776620 Reference: [4] Hodel R.E., Vaughan J.E.: Reflection theorems for cardinal functions.Topology Appl. 100 (2000), 47-66. Zbl 0943.54003, MR 1731704 Reference: [5] Ramírez-Páramo A.: A reflection theorem for i-weight.Topology Proc. 28 (2004), 1 277-281. Zbl 1079.54005, MR 2105463 Reference: [6] Tkachenko M.G.: Chains and cardinals.Soviet Math. Dokl. 119 (1978), 382-385. Zbl 0404.54002 .

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