http://dspace.nbuv.gov.ua:80/handle/123456789/150394 2026-04-21T07:51:07Z 2026-04-21T07:51:07Z Zhuchok, Y.V. http://dspace.nbuv.gov.ua:80/handle/123456789/155257 2019-06-16T22:28:49Z 2016-01-01T00:00:00Z

Automorphisms of the endomorphism semigroup of a free commutative g-dimonoid Zhuchok, Y.V. We determine all isomorphisms between the endomorphism semigroups of free commutative g-dimonoids and prove that all automorphisms of the endomorphism semigroup of a free commutative g-dimonoid are quasi-inner.

2016-01-01T00:00:00Z Protasov, I. Protasova, K. http://dspace.nbuv.gov.ua:80/handle/123456789/155256 2019-06-16T22:28:23Z 2016-01-01T00:00:00Z

The comb-like representations of cellular ordinal balleans Protasov, I.; Protasova, K. Given two ordinal λ and γ, let f:[0,λ)→[0,γ) be a function such that, for each α<γ, sup{f(t):t∈[0,α]}<γ. We define a mapping df:[0,λ)×[0,λ)⟶[0,γ) by the rule: if x<y then df(x,y)=df(y,x)=sup{f(t):t∈(x,y]}, d(x,x)=0. The pair ([0,λ),df) is called a γ−comb defined by f. We show that each cellular ordinal ballean can be represented as a γ−comb. In General Asymptology, cellular ordinal balleans play a part of ultrametric spaces.

2016-01-01T00:00:00Z Bardyla, S. Gutik, O. http://dspace.nbuv.gov.ua:80/handle/123456789/155255 2019-06-16T22:26:58Z 2016-01-01T00:00:00Z

On a semitopological polycyclic monoid Bardyla, S.; Gutik, O. We study algebraic structure of the λ-polycyclic monoid Pλ and its topologizations. We show that the λ-polycyclic monoid for an infinite cardinal λ≥2 has similar algebraic properties so has the polycyclic monoid Pn with finitely many n≥2 generators. In particular we prove that for every infinite cardinal λ the polycyclic monoid Pλ is a congruence-free combinatorial 0-bisimple 0-E-unitary inverse semigroup. Also we show that every non-zero element x is an isolated point in (Pλ,τ) for every Hausdorff topology τ on Pλ, such that (Pλ,τ) is a semitopological semigroup, and every locally compact Hausdorff semigroup topology on Pλ is discrete. The last statement extends results of the paper [33] obtaining for topological inverse graph semigroups. We describe all feebly compact topologies τ on Pλ such that (Pλ,τ) is a semitopological semigroup and its Bohr compactification as a topological semigroup. We prove that for every cardinal λ≥2 any continuous homomorphism from a topological semigroup Pλ into an arbitrary countably compact topological semigroup is annihilating and there exists no a Hausdorff feebly compact topological semigroup which contains Pλ as a dense subsemigroup.

2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155249 2019-06-16T22:28:19Z 2016-01-01T00:00:00Z

Mykola Komarnytskyi (25.05.1948 — 21.04.2016) Distinguished Professor of Ivan Franko L'viv National University, Doctor of Sciences Mykola Komarnytskyi passed away on April 21, 2016. His sudden death is a great loss for L'viv mathematicians and for the entire Ukrainian mathematics community.

2016-01-01T00:00:00Z