# Article

Full entry | PDF   (0.2 MB)
Keywords:
i-weight; reflection; T$_1$-separating weight; LOTS; compact
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 $\kappa$.
References:
[1] Engelking R.: General Topology. Helderman, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[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
[3] Hodel R.: Cardinal functions I. in: K. Kunen, J. Vaughan (Eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp.1-61. MR 0776620 | Zbl 0559.54003
[4] Hodel R.E., Vaughan J.E.: Reflection theorems for cardinal functions. Topology Appl. 100 (2000), 47-66. MR 1731704 | Zbl 0943.54003
[5] Ramírez-Páramo A.: A reflection theorem for i-weight. Topology Proc. 28 (2004), 1 277-281. MR 2105463 | Zbl 1079.54005
[6] Tkachenko M.G.: Chains and cardinals. Soviet Math. Dokl. 119 (1978), 382-385. Zbl 0404.54002

Partner of