In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to ...

The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not o...

In this thesis, we study continuum tree-valued processes. First, we define anabstract framework for these processes, by constructing a metric on the space of locally com-pact, complete R-trees, endowed with a locally finite Borel measure. This topology, calledGromov-Hausdorff-Prokhorov topology, allows for the definition of tree-valued Markov pro-cesses. We then give a new const...

Superconducting states with different internal topology are discussed for the layered high-T c materials. If the time inversion symmetry is broken, the superconductivity is determined not only by the symmetry of the superconducting state, but also by the topology of the ground state. The latter is determined the integer-valued momentum-space topological invariant N. The current carrying boundar...

Spaces of all entire functions f represented by vector valued Dirichlet series and having slow growth have been considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous transformations is characterized. Proper bases have also been characterized in terms of growth parameters.

Sufficient conditions ensuring weak lower semi-continuity of the optimal value function are presented. To this end, refined inner semi-continuity properties of set-valued maps are introduced which meet the needs of the weak topology in Banach spaces. The results are applied to prove the existence of solutions in various worst-case robust optimal control problems governed by semilinear elliptic ...

We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

This paper considers metrics valued in abelian `-groups and their induced topologies. In addition to a metric into an `-group, one needs a filter in the positive cone to determine which balls are neighborhoods of their center. As a key special case, we discuss a topology on a lattice ordered abelian group from the metric dG and the filter of positives consisting of the weak units of G; in the c...

We prove a rank-dependent moderate deviation principle for Uempirical measures, where the underlying i. i. d. random variables take values in a measurable (not necessarily Polish) space (S,S). The result can be formulated on a suitable subset of all signed measures on (Sm,S⊗m). We endow this space with a topology, which is stronger than the usual τ -topology. A moderate deviation principle for ...

We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a semigroup already implies (local/quasi) equicontinuity. We apply our results to transition semigroups and show that, under suitable hypothesis on E, every transition semigroup on Cb(E) which is conti...