A note on the Bohr compactification.
A note on the embedding of topological semigroups.
A note on the location of joint discontinuity.
A note on the support of right invariant measures.
A note on the WAP-compactification of groups.
A note on topological model theory
A notion of open generalized morphism that carries amenability.
A quest for nice kernels of neighbourhood assignments
Given a topological property (or a class) , the class dual to (with respect to neighbourhood assignments) consists of spaces such that for any neighbourhood assignment there is with and . The spaces from are called dually . We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define -spaces. We prove a number of results on duals of some general classes of spaces establishing, in particular, that any generalized ordered space...
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark on compact semi lattices of groups.
A separately, but not jointly continuous action of a compact semilattice.
A simple characterization of sets satisfying the central sets theorem.
A solenoidal and monothetic minimally almost periodic group
A solution to Comfort's question on the countable compactness of powers of a topological group
In 1990, Comfort asked Question 477 in the survey book “Open Problems in Topology”: Is there, for every (not necessarily infinite) cardinal number , a topological group G such that is countably compact for all cardinals γ < α, but is not countably compact? Hart and van Mill showed in 1991 that α = 2 answers this question affirmatively under . Recently, Tomita showed that every finite cardinal answers Comfort’s question in the affirmative, also from . However, the question has remained...
A Structure On A Set Of Subsets
A survey of compact divisible commutative semigroups.
A survey on just-non- groups.
A uniquely homogeneous space need not be a topological group
A Vanishing Theorem for Group Compactifications.
Abelian pro-countable groups and orbit equivalence relations
We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups....