Filter spaces and continuous functionals

Continuous Functionals of Dependent Types and Equilogical Spaces

We show that dependent sums and dependent products of continuous parametrizations on domains with dense, codense, and natural totalities agree with dependent sums and dependent products in equilogical spaces, and thus also in the realizability topos RT(Pω).

Additive functionals on spaces with non-absolutely-continuous norm

Order continuous linear functionals on non-locally convex Orlicz spaces

The space of all order continuous linear functionals on an Orlicz space L defined by an arbitrary (not necessarily convex) Orlicz function φ is described.

Equilogical spaces and filter spaces

The paper is about the comparison between (apparently) different cartesian closed extensions of the category of topological spaces. Since topological spaces do not in general allow formation of function spaces, the problem of determining suitable categories with such a property—and nicely related to that of topological spaces—was studied from many different perspectives: general topology, funct...

Banach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support

In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.