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Keywords:
i-weight; reflection; T$_1$-separating weight; LOTS; compact
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:
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