For a locally compact Hausdorff semigroup S, the L representation algebra R(S) was extensively studied by Dunkl and Ramirez. The FourierStieltjes algebra F (S) of a topological semigroup was studied by Lau. The aim of this paper is to investigate these two algebras and study the amenability of them with respect to the structure of S.

An example of a D-metric space is given, in which D-metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructing D-metric spaces from a given metric space are developed and are used in constructing (1) an example of a D-metric space in which D-metric convergence defines a topology which is T1 but not Hausdorff...

The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced.We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, ...

If G is a locally compact topological group, let BC{G) denote the set of real-valued, bounded, uniformly continuous functions on G with the compact-open topology. Using the fact that the distal (weakly distal) functions are the elements of BC(G) whose orbit closures are compact distal (point-distal) minimal sets, we can characterize compact distal and point-distal minimal transformation groups....

We study the set of bounded geodesies of hyperbolic manifolds. For general Riemann surfaces and for hyperbolic manifolds with some finiteness assumption on their geometry we determine its Hausdorff dimension. Some applications to diophantine approximation are included.

On the surface, the definitions of chainability and Lebesgue covering dimension ≤ 1 are quite similar as covering properties. Using the ultracoproduct construction for compact Hausdorff spaces, we explore the assertion that the similarity is only skin deep. In the case of dimension, there is a theorem of E. Hemmingsen that gives us a first-order lattice-theoretic characterization. We show that ...

We study similarity classes of point configurations in R. Given a finite collection of points, a well-known question is: How high does the Hausdorff dimension dimH(E) of a compact set E ⊂ R, d ≥ 2, need to be to ensure that E contains some similar copy of this configuration? We prove results for a related problem, showing that for dimH(D) sufficiently large, E must contain many point configurat...

In this paper, we shall prove three equilibrium existence theorems for generalized games in Hausdorff topological vector spaces.

We give a geometric proof of the following well-established theorem for o-minimal expansions of the real field: the Hausdorff limits of a compact, definable family of sets are definable. While previous proofs of this fact relied on the model-theoretic compactness theorem, our proof explicitely describes the family of all Hausdorff limits in terms of the original family.

We introduce a quasiregular analog F of the sine and cosine function such that, for a sufficiently large constant λ, the map x 7→ λF (x) is locally expanding. We show that the dynamics of this map define a representation of Rd, d ≥ 2, as a union of simple curves γ : [0,∞) → Rd which tend to ∞ and whose interiors γ∗ = γ((0,∞)) are disjoint such that the union of all γ∗ has Hausdorff dimension 1.