Nonstandard topological extensions

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

Extensions of Topological Algebras

We prove that, in the class of commutative topological algebras with separately continuous multiplication, an element is permanently singular if and only if it is a topological divisor of zero. This extends the result given by R. Arens [1] for the Banach algebra case. We also give sufficient conditions for non-removability of ideals in commutative topological algebras with jointly continuous mu...

Brandt extensions and primitive topologically periodic inverse topological semigroups

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

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 and standard compactifications of ordered topological spaces

Salbany, S. and T. Todorov, Nonstandard and standard cornpactifications of ordered topological spaces, Topology and its Applications 47 (1992) 35-52. We construct the Nachbin ordered compactification and the ordered realcornpactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of mon...