In this paper, we establish a connection between categorical closedness and
nontopologizability of semigroups. In particular, for the class 𝖳 𝟣⁢ 𝖲 of T 1 topological …

This is a survey on the recent progress in minimal topological groups, with a particular
emphasis on constructions leading to non-abelian minimal groups, as semidirect products …

This book provides an introduction to topological groups and the structure theory of locally
compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality …

These notes provide a brief introduction to topological groups with a special emphasis on
Pontryagin-van Kampen's duality theorem for locally compact abelian groups. We give a …

Every proper closed subgroup of a connected Hausdorff group must have index at least c,
the cardinality of the continuum. 70 years ago Markov conjectured that a group G can be …

Publisher Summary This chapter discusses selected topics from the structure theory of
topological groups. It contains open problems and questions covering the a number of topics …

In this paper we explore the extent to which the algebraic structure of a monoid $ M $
determines the topologies on $ M $ that are compatible with its multiplication. Specifically we …

Every group G carries an intrinsically defined (by means of solution sets of one-variable
equations) topology ZG, named Zariski topology. It is related to another topology MG having …

We give a necessary and sufficient condition, in terms of a certain reflection principle, for
every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove …

We prove that an abelian group admits a minimally almost periodic (MinAP) group topology
if and only if it is connected in its Markov-Zariski topology. In particular, every unbounded …