On an algebraic version of Tamano’s theorem

Abstract

Let X be a non-paracompact subspace of a linearly ordered topological space. We prove, in particular, that if a Hausdorff topological group G contains closed copies of X and a Hausdorff compactification bX of X then G is not normal. The theorem also holds in the class of monotonically normal spaces.

Keywords

• Topological group, Hausdorff compactification
• Normal space
• Stationary set