Two Examples of Q-topologies
Two examples of Q-topologies.
Two types of remainders of topological groups
We prove a Dichotomy Theorem: for each Hausdorff compactification of an arbitrary topological group , the remainder is either pseudocompact or Lindelöf. It follows that if a remainder of a topological group is paracompact or Dieudonne complete, then the remainder is Lindelöf, and the group is a paracompact -space. This answers a question in A.V. Arhangel’skii, Some connections between properties of topological groups and of their remainders, Moscow Univ. Math. Bull. 54:3 (1999), 1–6. It is...