4 citations · 6 across the 13 of their papers we have counts for
13 papers
Detecting the real line among one-parametric topological groups
Taras Banakh, Kateryna Makarova, Oles Mazurenko
We prove that a topological group is isomorphic to the real line if and only if it is a one-parameteric, metrizable, and not monothetic. This result is used in the authors' other p…
On regular operators extending (pseudo)metrics
Taras Banakh
It is proved that for every stratifiable space and a closed subset there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\…
Steiner systems and exist
Taras Banakh, Ivan Hetman, Alex Ravsky
Via computer search, we found seven non-isomorphic -rotational Steiner systems and six point-transitive Steiner systems , resolving two of previous…
Locally compact strictly convex metric groups are abelian
Taras Banakh, Oles Mazurenko
We show that every locally compact strictly convex metric group is abelian, thus answering one problem posed by the authors in their earlir paper. To prove this theorem we first co…
Plastic metric spaces and groups
Taras Banakh, Oles Mazurenko, Olesia Zavarzina
A metric space is plastic if all its non-expansive bijections are isometries. We prove three main results: (1) every countable dense subspace of a normed space is not plastic, (2)…
A topological approach to fuzzy iterated function systems
Taras Banakh, Krzysztof Caban, Filip Strobin
In the paper we unify two extensions of the classical Hutchinson--Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuz…