A note on the Bohr compactification.
A question raised in R. G. Woods' paper has a simple solution.
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 prove the addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.