
W. W. COMFORT, Wesleyan University 
Continuous cross sections on abelian groups equipped with the Bohr topology 
All groups here are Abelian. A closed subgroup H of a topological group G is a ccssubgroup if there is a continuous cross section from G/H to Gthat is, a continuous function such that (with the natural homomorphism).
The symbol denotes G with its Bohr topology, i.e., the topology induced by .
A topological group H is an absolute ccsgroup [resp., an absolute retract ] if His a ccssubgroup [resp., is a retract] in every group of the form containing H as a (necessarily closed) subgroup. One then writes [resp., ].
Theorem 1. Every
ccssubgroup H of a group of the form
is a retract of (and is homeomorphic to
); hence
.
Theorem 2.
[resp.,
] iff is a
ccssubgroup of its
divisible hull
[resp., is a
retract of
].
Theorem 3. (a) Every cyclic group is in
.
(b) The classes
and
are closed
under finite products.
Theorem 4. Not every Abelian group is in
.
Question [van Douwen, 1990]. Is every Abelian group in ?
^{*} Presented in Kingston by this coauthor.