Hausdorff Nonstandard Extensions

Extensions of Hausdorff Spaces

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

Hausdorff Measures and Two Point Set Extensions

We investigate the question: under which conditions is a-compact partial two point contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a suucient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any-compact partial two point set such that ...

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...

Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications

Let (X,T ) be a topological space, and X a non–standard extension of X . There is a natural “standard” topology T on X generated by G, where G ∈ T . The topological space ( X, T ) will be used to study, in a systematic way, compactifications of (X,T ) . Mathematics Subject Classification: 031105, 54J05, 54D35, 54D60.