In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilatti...

This paper studies separating subsets of an invariant ring or, more generally, of any set consisting of functions. We prove that a subset of a finitely generated algebra always contains a finite separating subset. We also show that a general version of Noether’s degree bound holds for separating invariants, independently of the characteristic. The paper also contains a conceptual investigation ...

We consider predicative type-abstraction disciplines based on type quantification with finitely stratified levels. The main technical result is that the functions representable in the finitely stratified polymorphic A-calculus are precisely the super-elementary functions, i.e. the class £4 in Grzegorczyk's subrecursive hierarchy. This implies that there is no super-elementary bound on the lengt...

Contents 1. Introduction 2. Real closed rings-a model theoretic tour 3. Computation of the z-radical in C(X) 4. A sentence in the language of rings separating continuous semi-algebraic from arbitrary continuous functions 5. Super real closed rings: Definition and basic properties 6. Υ-ideals 7. Localization of super real closed rings 8. Application: o-minimal structures on super real closed fie...

Stone-Weierstrass-type theorems for groups of group-valued functions with discrete range or discrete domain are obtained. We study criteria for a subgroup of the group of continuous functions C(X,G) (X compact, G a topological group) to be uniformly dense. These criteria are based on the existence of so-called condensing functions, where a continuous function φ : G → G is said to be condensing ...

A finitely generated group G is called representation rigid (briefly, rigid) if for every n, G has only finitely many classes of simple C representations in dimension n. Examples include higher rank S-arithmetic groups. By Margulis super rigidity, the latter have a stronger property: they are representation super rigid; i.e., their proalgebraic completion is finite dimensional. We construct exa...

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length ≤ n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results.

By using generalized Salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. Coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

We define the strongly separating curve graph to be the full subgraph of the curve graph of a compact orientable surface, where the vertex set consists of all separating curves which do not bound a three-holed sphere. We show that, for all but finitely many surfaces, any automorphism of the strongly separating curve graph is induced by an element of the mapping class group.