arXiv subjects

O. Hryniv

Publications and source records attributed to O. Hryniv.

3 recordsLinked to original sources

arXiv2012

On closed embeddings of free topological algebras

Let $\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\mathcal E$ (which means that $\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all completely regular topological $\mathcal E$-algebras algebraically isomorphic to members of $\mathcal K$). For a topological space $X$ by $F(X)$ we denote the free universal $\mathcal E$-algebra over $X$ in the class $\mathcal K$. Using some extension properties of the Hartman-Mycielski construction we prove that for a closed subspace $X$ of a metrizable (more generally, stratifiable) space $Y$ the induced homomorphism $F(X)\to F(Y)$ between the respective free universal algebras is a closed topological embedding. This generalizes one result of V.Uspenskii concerning embeddings of free topological groups.

math.GN↗

arXiv2010

Long time behaviour in a model of microtubule growth

We study a continuous time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (global) hydrolysis processes. We give a complete characterization of the phase diagram of the model, and derive several criteria of the transient and recurrent regimes for the underlying stochastic process.

math.PR↗

arXiv2008

Free topological inverse semigroups as infinite-dimensional manifolds

Let $K$ be a complete quasivariety of topological inverse Clifford semigroups, containing all topological semilattices. It is shown that the free topological inverse semigroup $F(X,K)$ of $X$ in the class $K$ is an $R^\infty$-manifold if and only if $X$ has no isolated points and $F(X,K)$ is a retract of an $R^\infty$-manifold. We derive from this that for any retract $X$ of an $R^\infty$-manifold the free topological inverse semigroup $F(X,K)$ is an $R^\infty$-manifold if and only if the space $X$ has no isolated points. Also we show that for any homotopically equivalent retracts $X,Y$ of $R^\infty$-manifolds with no isolated points the free topological inverse semigroups $F(X,K)$ and $F(Y,K)$ are homeomorphic. This allows us to construct non-homeomorphic spaces whose free topological inverse semigroups are homeomorphic.

math.GN↗