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We study some topological properties of attractors.
Some boundedness properties of function spaces (considered as topological groups) are studied.
We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition…
We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
We study when the fiber product of groups with Property (T) has Property (T).
Given a subset of real numbers $A$ with small product $AA$ we obtain a new upper bound for the additive energy of $A$. The proof uses a natural observation that level sets of convolutions of the characteristic function of $A$ have small…
Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
We find many conditions equivalent to the model-theoretical property $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in [L1]. Our conditions involve uniformity of ultrafilters, compactness properties of products of topological…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that…
We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also…
We consider Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogous to the additive functional equation on a group. We show, among other things, that our generalized…
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…
I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible…
Starting from a plausible assumption about the Total Revenue concept, a system of economic agents, that simulates the exchange of goods, is studied. Following a methodology equivalent to that used in the statistical-mechanical determination…
We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older…
We report a simple rigidity theorem for certain Euler products.
This note contains a Stone-style representation theorem for compact Hausdorff spaces.