Some compactifications of a semitopological semigroup.
Some conditions under which a continuous semigroup morphism is strongly differentiable.
Some continua admitting only trivial multiplications.
Some examples of clans.
Some examples of monothetic groups
Some finitely generated subsemigroups of S(X)
Some large and small sets in topological groups.
Some Minimal Group Topologies are Precompact.
Some remarks on subgroups defined by the Bohr compactification.
Some remarks on topologically semiprime ideals
Some results on compact convergence semigroups defined by filters.
Some theorems on hemigroups.
Spaces and equations
It is proved, for various spaces A, such as a surface of genus 2, a figure-eight, or a sphere of dimension ≠ 1,3,7, and for any set Σ of equations, that Σ cannot be modeled by continuous operations on A unless Σ is undemanding (a form of triviality that is defined in the paper).
Split ...-coextensions of topological inverse semigroups.
Stability of strongly continuous representations of abelian semigroups.
Stabilizers of closed sets in the Urysohn space
Building on earlier work of Katětov, Uspenskij proved in [8] that the group of isometries of Urysohn's universal metric space 𝕌, endowed with the pointwise convergence topology, is a universal Polish group (i.e. it contains an isomorphic copy of any Polish group). Answering a question of Gao and Kechris, we prove here the following, more precise result: for any Polish group G, there exists a closed subset F of 𝕌 such that G is topologically isomorphic to the group of isometries of 𝕌 which map...
Standard threads and distributivity.
Strict completions of -groups
Strong continuity of semigroup homomorphisms
Let J be an abelian topological semigroup and C a subset of a Banach space X. Let L(X) be the space of bounded linear operators on X and Lip(C) the space of Lipschitz functions ⨍: C → C. We exhibit a large class of semigroups J for which every weakly continuous semigroup homomorphism T: J → L(X) is necessarily strongly continuous. Similar results are obtained for weakly continuous homomorphisms T: J → Lip(C) and for strongly measurable homomorphisms T: J → L(X).
Strong morphisms of groupoids.