The a-congruences on S(X) and the S-equivalences on X.
The automorphism group of the Lebesgue measure has no non-trivial subgroups of index
We show that the automorphism group Aut([0,1],λ) of the Lebesgue measure has no non-trivial subgroups of index .
The Baire property in remainders of topological groups and other results
It is established that a remainder of a non-locally compact topological group has the Baire property if and only if the space is not Čech-complete. We also show that if is a non-locally compact topological group of countable tightness, then either is submetrizable, or is the Čech-Stone remainder of an arbitrary remainder of . It follows that if and are non-submetrizable topological groups of countable tightness such that some remainders of and are homeomorphic, then the spaces...
The Banach contraction mapping principle and cohomology
By a dynamical system we mean the action of the semigroup on a metrizable topological space induced by a continuous selfmap . Let denote the set of all compatible metrics on the space . Our main objective is to show that a selfmap of a compact space is a Banach contraction relative to some if and only if there exists some which, regarded as a -cocycle of the system , is a coboundary.
The congruences on S(X) which commute with V.
The equicontinuous structure relation of a unicoherent point-transitive flow
The equivariant universality and couniversality of the Cantor cube
Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding ; (2) there exists an embedding , equivariant with respect to φ, such that ψ(X) is an equivariant retract of with respect to φ...
The largest proper congruence on S(X).
The largest proper regular ideal of
The local contractibility of the homeomorphism space of a 2-polyhedron
The local weight of an effective locally compact transformation group and the dimension of
The monomorphism semigroup of S(X).
The partially ordered collection of regular ...-classes of S(X).
The quantum double of a (locally) compact group.
The topology of the unit interval is not uniquely determined by its continuous self maps among set systems
The universal semilattice compactification of a semigroup.
Topological Galois spaces
Topological semigroups and Kirk's question
Topologies on the Group of Self Homeomorphisms of the Cantor Set
Transformation groups with no equicontinuous minimal set