Bornological Completion of Locally Convex Cones

Some Results on Boundedness in Locally Convex Cones

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

some results on boundedness in locally convex cones

Locally Lipschitz Functions and Bornological Derivatives

We study the relationships between Gateaux, Weak Hadamard and Fréchet differentiability and their bornologies for Lipschitz and for convex functions. AMS Subject Classification. Primary: 46A17, 46G05, 58C20. Secondary: 46B20.

Locally convex cones and the Schröder-Simpson Theorem

At MFPS 23 at Birmingham, Schröder and Simpson had announced a result that I did not absorb at the time. A special case of that theorem for stably compact spaces was announced by Cohen, Escardo and the author shortly afterwards. I did not believe in the theorem of Schröder and Simpson until I saw a proof that they showed to me in detail during a visit to Edinburgh. At the New Interactions Works...

Boundedness and Connectedness Components for Locally Convex Cones

We introduce topologies on locally convex cones which are in general coarser than the given topologies and take into account the presence of unbounded elements. Using these topologies, we investigate relations between the connectedness and the boundedness components of a locally convex cone.