7 papers
Precompact groups and convergence
Alexander Shibakov
We consider precompact sequential and Fréchet group topologies and show that some natural constructions of such topologies always result in metrizable groups answering a question o…
Countably compact groups and sequential order
Dmitri Shakhmatov, Alexander Shibakov
We use to construct, for every a sequential countably compact topological group of sequential order . This establishes the independence of the existenc…
Scott functions, their representations on domains, and applications to random sets
Motoya Machida, Alexander Shibakov
Choquet theorems (1954) on integral representation for capacities are fundamental to probability theory. They inspired a growing body of research into different approaches and gene…
Stack and register complexity of radix conversions
Motoya Machida, Alexander Shibakov
We investigate the question of computational resources (such as stacks and counters) necessary to perform radix conversions. To this end it is shown that no PDA can compute the sig…
On large sequential groups
Alexander Shibakov
We construct, using , an example of a sequential group such that the only countable sequential subgroups of are closed and discrete, and the only quotients of…
On sequential analytic groups
Alexander Shibakov
We answer a question of S.~Todorčević and C.~Uzcátegui from \cite{TU1} by showing that the only possible sequential orders of sequential analytic groups are and . Other re…