Brad Bailey
I-weight of compact and locally compact LOTS

Comment.Math.Univ.Carolin. 48,4 (2007) 677-688.

Abstract:Ram\'{\i }rez-P\'aramo 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 $.

Keywords: i-weight, reflection, T$_1$-separating weight, LOTS, compact
AMS Subject Classification: 54A25, 54F05