Semigroups with [ x] [ y] = [y][x].
Semilattice structures on trees.
Semilattices which are embeddable in a product of min intervals.
Semilattices which must contain a copy of 2 N.
Seminormed spaces
Semi-quotient mappings and spaces
In this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.
Semirings on cones.
Semi-Topological Groups and Linear Spaces.
Semitopological homomorphisms
Sequential convergences in distributive lattices
In this paper we investigate the system Conv of all sequential convergences on a distributive lattice .
Sequential convergences in lattices
The notion of sequential convergence on a lattice is defined in a natural way. In the present paper we investigate the system of all sequential convergences on a lattice .
Sequentially determined convergence spaces
Set-set topologies and semitopological groups.
Sizes of quotient spaces of certain function algebras on topological semigroups
SL(2) has no C1-extension to a half-space.
Smooth quasigroups and loops: forty-five years of incredible growth
The remarkable development of the theory of smooth quasigroups is surveyed.
Solution of Belousov's problem
The authors prove that a local n-quasigroup defined by the equation , where , i,j = 1,...,n, are arbitrary functions, is irreducible if and only if any two functions and , i ≠ j, are not both linear homogeneous, or these functions are linear homogeneous but . This gives a solution of Belousov’s problem to construct examples of irreducible n-quasigroups for any n ≥ 3.
Solution of distributive-like quasigroup functional equations
We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like quasigroup...
Some algebraic universal semigroup compactifications.
Some aspects of nuclear vector groups
In [2] W. Banaszczyk introduced nuclear groups, a Hausdorff variety of abelian topological groups which is generated by all nuclear vector groups (cf. 2.3) and which contains all nuclear vector spaces and all locally compact abelian groups. We prove in 5.6 that the Hausdorff variety generated by all nuclear vector spaces and all locally compact abelian groups (denoted by 𝒱₁) is strictly smaller than the Hausdorff variety of all nuclear groups (denoted by 𝒱₂). More precisely,...