A characterization of strongly countably complete topological groups

We prove that a topological group G is strongly countably complete (the notion introduced by Z. Frolik in 1961) iff G contains a closed countably compact subgroup H such that the quotient space G/H is completely metrizable and the canonical mapping pi : G -> G/H is closed. We also show that every strongly countably complete group is sequentially complete, has countable G(delta)-tightness, and its completion is a tech-complete topological group. Further, a pseudocompact strongly countably complete group is countably compact. An example of a pseudocompact topological Abelian group H with the Frechet-Urysohn property is presented such that H fails to be sequentially complete, thus answering a question posed by Dikranjan, Martin Peinador, and Tarieladze in [Appl. Categor. Struct. 15 (2007) 511-539]. (C) 2012 Elsevier B.V. All rights reserved.