We study closed subspaces of -Ohio complete spaces and, for uncountable cardinal, we prove a characterization for them. We then investigate the behaviour of products of -Ohio complete spaces. We prove that, if the cardinal is endowed with either the order or the discrete topology, the space is not -Ohio complete. As a consequence, we show that, if is less than the first weakly inaccessible cardinal, then neither the space , nor the space is -Ohio complete.
We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space , every remainder of is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.
We present several sum theorems for Ohio completeness. We prove that Ohio completeness is preserved by taking σ-locally finite closed sums and also by taking point-finite open sums. We provide counterexamples to show that Ohio completeness is preserved neither by taking locally countable closed sums nor by taking countable open sums.
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