Imbedding of an $n$-Dimensional Topological Group by Michael Zarichnyi

Topology Atlas Document # qaaa-01 | Production Editor: Harriet Lord

Question
Imbedding of an n-Dimensional Topological Group
Michael Zarichnyi
Answered in The completion of Q^N provides an answer to a question of Zarichnyi by Dmitri Shakhmatov

Guran and I proved that there exists a countable-dimensional (separable metrizable) topological group which contains every finite-dimensional topological group whose underlying space is G_\delta. The following question arises:

Can every n-dimensional topological group be imbedded as a (not necessarily closed) subgroup of an n-dimensional group whose underlying space is an absolute G_\delta? (All groups are assumed to be separable metrizable.)

Received by the editors: January 2, 1996