Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Oleg Gutik"'
Autor:
Oleg Gutik, Anatolii Savchuk
Publikováno v:
Pracì Mìžnarodnogo Geometričnogo Centru, Vol 12, Iss 3, Pp 51-68 (2019)
In this paper we study the structure of the monoid Iℕn ∞ of cofinite partial isometries of the n-th power of the set of positive integers ℕ with the usual metric for a positive integer n > 2. We describe the group of units and the subset of ide
Externí odkaz:
https://doaj.org/article/d3f42d681b964670ae18e007c59c7fee
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2010 (2010)
We study (countably) compact and (absolutely) 𝐻-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topo
Externí odkaz:
https://doaj.org/article/4921f02309a84c81bc73f3c5a8c5d310
Autor:
Oleg Gutik, Pavlo Khylynskyi
Publikováno v:
Topological Algebra and its Applications. 10:233-245
Let 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofi
Autor:
O. Yu. Sobol, Oleg Gutik
Publikováno v:
Journal of Mathematical Sciences. 254:13-20
We study feebly compact shift-continuous topologies on the semilattice (expn λ;∩). It is shown that a T1-topology of this kind is sequentially pracompact if and only if it is (ω)-compact.
Publikováno v:
Topological Algebra and its Applications, Vol 8, Iss 1, Pp 76-87 (2020)
A topological semigroup is monothetic provided it contains a dense cyclic subsemigroup. The Koch problem asks whether every locally compact monothetic monoid is compact. This problem was opened for more than sixty years, till in 2018 Zelenyuk obtaine
Autor:
Serhii Bardyla, Oleg Gutik
Publikováno v:
Algebra and Discrete Mathematics. 30:26-43
A Hausdorff topology \(\tau\) on the bicyclic monoid with adjoined zero \(\mathcal{C}^0\) is called weak if it is contained in the coarsest inverse semigroup topology on \(\mathcal{C}^0\). We show that the lattice \(\mathcal{W}\) of all weak shift-co
Autor:
Anatolii Savchuk, Oleg Gutik
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 11, Iss 2, Pp 296-310 (2019)
In this paper we study submonoids of the monoid $\mathscr{I}_\infty^{\,\Rsh\!\!\!\nearrow}(\mathbb{N})$ of almost monotone injective co-finite partial selfmaps of positive integers $\mathbb{N}$. Let $\mathscr{I}_\infty^{\!\nearrow}(\mathbb{N})$ be a
Autor:
Anatolii Savchuk, Oleg Gutik
Publikováno v:
Pracì Mìžnarodnogo Geometričnogo Centru, Vol 12, Iss 3, Pp 51-68 (2019)
In this paper we study the structure of the monoid Iℕn ∞ of cofinite partial isometries of the n-th power of the set of positive integers ℕ with the usual metric for a positive integer n > 2. We describe the group of units and the subset of ide
Autor:
Oleg Gutik, Taras Mokrytskyi
Publikováno v:
European Journal of Mathematics. 6:14-36
Let n be any positive integer and be the semigroup of all order isomorphisms between principal filters of the nth power of the set of positive integers $${\mathbb {N}}$$ with the product order. We study algebraic properties of the semigroup . In part
Autor:
Kateryna Maksymyk, Oleg Gutik
Publikováno v:
Journal of Mathematical Sciences. 238:32-45
For a linearly ordered group $G$ let us define a subset $A\subseteq G$ to be a \emph{shift-set} if for any $x,y,z\in A$ with $y < x$ we get $x\cdot y^{-1}\cdot z\in A$. We describe the natural partial order and solutions of equations on the semigroup