Coarse topologies in nonstandard extensions via separative ultrafilters

Coarse Geometry via Grothendieck Topologies

In the course of the last years several authors have studied index problems for open Riemannian manifolds. The abstract indices are elements in the K-theory of an associated C∗-algebra, which only depends on the ”coarse” (or large scale) geometry of the underlying metric space. In order to make these indices computable J.Roe introduced a new cohomology theory, called coarse cohomology, which is...

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

On extensions of fuzzy topologies

The concept of fuzzy topological spaces was introduced in [2] and ever since this introduction much research has been done in this area. In this note we introduce the concept of extension of fuzzy topological spaces as done for topological spaces in [1,7]. Let (X, T) be a fuzzy topological space and T C T*. Then T* will be called a simple extension of T iff there exists a 6 $T such that T* = {A...

Uniform Symbolic Topologies and Finite Extensions

We study the behavior of rings with uniform symbolic topologies with respect to finite extensions.

Isomorphism property in nonstandard extensions of ZFC universe

We study 1 models of HST (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata and Saturation for well-orderable families of internal sets). This theory admits an adequate formulation of the isomorphism property IP : any two elementarily equivalent internally presented structures of a well-orderable language are isomorphic. IP implies, for instance...