相关论文: Topological Test Spaces

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

As defined by Dunn, Moss, and Wang, an universal test set in an ortholattice $L$ is a subset $T$ such that each term takes value $1$, only, if it does so under all substitutions from $T$. Generalizing their result for ortholattices of…

This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…

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…

We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…

We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical…

Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…

In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…