This article is a revised version of notes on an advanced course given in Liverpool from
January to March 1977 in preparation for the symposium. The lectures given by Terry Wall at …

A subset A of a topological group G is said to be totally bounded if for any neighborhood U of
the identity there exists a finite subset K c G such that A~(KU N UK). If the subset G of a …

Purdue University Page 1 FREE TOPOLOGICAL, GROUPS A Thesis Submitted to the Faculty
of Purdue University by Robert Lee Cooley In Partial Fulfillment of the Requirements for the …

oup_qmathj_hay039 201..224 ++ Page 1 The Quarterly Journal of Mathematics Advance
Access published on September 4, 2018 Quart. J. Math. 70 (2019), 201–224; doi:10.1093/qmath/hay039 …

We define a variety V, of topological groups to be a family of topological groups closed
under cartesian products, quotient groups and subgroups. The class of groups, which with …

THEOREM 3. If G is locally compact, G'compact, and G has a closed abelian subgroup G1
such that G/G1G'is compact, then G is the semi-direct produict of H by V, where H has no …

In the first four sections of this chapter the law of composition of a group will generally be
written multiplicatively, and e shall denote the identity element; translation of results into …

1. Introduction. Let Oa, aeA, be an infinite set of groups. It is well known that there exist two
direct products of this set of groups, the restricted direct product and the unrestricted direct …

CLASSICAL TOPOLOGY AND COMBINATORIAL GROUP THEORY (Graduate Texts in
Mathematics, 72) Page 1 BOOK REVIEWS 77 CLASSICAL TOPOLOGY AND …

Let~ and G~ be topological groups,~(Q) and~(&#) the lattices of their closed subgroups with
the operations of intersection~ and generation V• A dualltv (dualism) of onto &@ is a …