Algebraic Transformation Groups and Representation.
Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows
Let be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of is Borel isomorphic to an almost 1-1 extension of . Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly ergodic toeplitz...
Almost all submaximal groups are paracompact and σ-discrete
We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.
Almost continuous functions on
Almost fixed points of semigroups of non-expansive mappings
Almost lower semicontinuous multifunctions and the Souslin-graph theorem
Almost maximal topologies on groups
Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
We prove that the interval topology of an Archimedean atomic lattice effect algebra is Hausdorff whenever the set of all atoms of is almost orthogonal. In such a case is order continuous. If moreover is complete then order convergence of nets of elements of is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on corresponding to compact and cocompact elements....
Almost periodic motion in complete space.
Almost-Topological Representation Theorems for Dynamical Systems.
Always of the first category sets
Always of the first category sets (II)
Amenability and unique ergodicity of automorphism groups of Fraïssé structures
In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering , where is the countably infinite-dimensional...
An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions
We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...
An algebraic and logical approach to continuous images
An analogon of the fixed-point theorem and its application for graphs
An analytic equivalence relation not arising from a Polish group action
An application of fixed-point theory to equilibrium analysis
An application of KKM-map principle.
An Application of the Stiefel-Whitney Classes to the Proof of a Fixed Point Theorem for Set-Valued Mappings
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.