In an L-topological space we present good definitions for local compactness, weak local compactness and relative local compactness. We obtain the equivalence of these properties in a Hausdorff space and we also obtain a one point compactification theorem.

We compare several parametrized analytic expressions for an arbitrary off-shell one-loop n-point function in scalar field theory in D-dimensional space-time, and show their equivalence both directly and through path-integral methods.

Let PCFk denote the sublanguage of Plotkin’s PCF in which fixed point operators Yσ are admitted only for types σ of level at most k. We show that the languages PCFk form a strict hierarchy as regards expressivity, in the sense that for each k, there are closed programs of PCFk+1 that are not observationally equivalent to any programs of PCFk. This answers positively a question posed by Berger i...

— In the usual framework of abstract types programming languages inciuding a définition mechanism for partial recursive functions cannot be specified sufficiently complete because of the termination problem. Therefore the algebraic concepts of abstract types are extended to partial algebras leading to "total" homomorphisms for partial algebras. In this framework an abstract type is given defini...

We explore a non-classical, universal set theory, based on a purely “structural” conception of sets. A set is a transfinite process of unfolding of an arbitrary (possibly large) binary structure, with identity of sets given by the observational equivalence between such processes. We formalize these notions using infinitary modal logic, which provides partial descriptions for set structures up t...

The path category P (X) of a simplicial set X defines a functor X 7→ P (X) which is left adjoint to the nerve functor B : cat → sSet. The first section of this paper contains an elementary description of this functor, with some of its basic properties. This construction specializes to a path category functor for cubical sets which appears in the second section. The path category construction is...