相关论文: Weak and local versions of measurability

We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in…

We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…

Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\mathcal{L}_{\kappa,\kappa}$. Using this equivalence we…

We introduce a covering notion depending on two cardinals, which we call $\mathcal O $-$ [ \mu, \lambda ]$-compactness, and which encompasses both pseudocompactness and many other generalizations of pseudocompactness. For Tychonoff spaces,…

We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…

Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…

In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting…

This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued…

In analogy with the classical theory of filters, for fi\-nite\-ly complete or small cat\-e\-go\-ries, we provide the concepts of fil\-ter, $\mathfrak{G}$-neigh\-bor\-hood (short for "Grothendieck-neigh\-bor\-hood") and…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…

We define separating properties for normal ultrafilters. We prove that compactness and supercompactness are separable, yet compactness and measurability are not. We describe how to use separating properties in order to elicit distinct…

Some recent attempts at measuring non local weak values via local measurements are discussed and shown to be less robust than standard weak measurements. A method for measuring some non local weak values via non local measurements (non…

We characterize the situation of small cardinality for a product of cardinals divided by an ultrafilter. We develop the notion of weak normality. We include an application to Boolean Algebras.

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…

Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…