Locally convex infinitesimal calculus. 2. Computations on Mackey (l∞)

On Subdifferential Calculus for Convex Functions Defined on Locally Convex Spaces

The subdifferential formula for the sum of two convex functions defined on a locally convex space is proved under a general qualification condition. It is proved that all the similar results which are already known can be derivated from the formula.

Some Results on Boundedness in Locally Convex Cones

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Lecture 19: Constructive Reals and Infinitesimal Calculus

We will present a very interesting theorem from Bishop and Bridges, and then we will briefly consider the nature of nonstandard models of the classical reals as presented in H.J. Keisler’s book, Elementary Calculus and his free 203 page instructor’s book entitled Foundations of the Infinitesimal Calculus [8] which is provided as a course resource with this lecture. We have not covered the basic...