Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we study the relationships between mset relations and mset topology. Moreover, this paper concerns generalized mset approximation spaces via topological methods ...

Can we do a topological study of various classes normal subgroups endowed with hull-kernel-type topology? In this paper, have provided an answer to question. We introduced as well new class called primitive subgroups. Separation axioms, compactness, connectedness, and continuities these spaces been studied . concluded the question determining spectral among them.

s of Past JMU REU Projects • Title. Partial Metric Spaces: Representation and Classification. (2014) Students. Shaun Benvie (University of Connecticut) and Owen Hill (William and Mary) Mentor. Elizabeth Brown Abstract. Partial metrics generalize the standard notion of distance, a metric, to allow for non-zero self-distances. We show how partial metrics can be constructed from standard metrics a...

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL0 over RCA0. We show that the separation theorem for separably closed convex sets is equivalent to ACA0 over RCA0. Our strategy for proving these geometrical Hahn–Banach...

Spatial logics have been used to describe properties of tree-like structures (Ambient Logic) and in a Hoare style to reason about dynamic updates of heap-like structures (Separation Logic). We integrate this work by analyzing dynamic updates to tree structures with pointers (such as XML with identifiers and idrefs). Naı̈ve adaptations of the previous logics are not expressive enough to capture s...

We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs or matroids, but can much more quite different. The asserts between the existence high somewhere local global overall tree structure. describe cohesive substructures in unified way format tangles: as orientations low-order separations satisfying certa...

We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react wh...

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. We then relate this weak metric to some familiar metrics such as the Poincaré metric, the Klein-Hil...

Based on the standard axioms of quantum theory, we provide a counterexample which invalidates the full compatibility between consciousness and quantum theory. In particular, we present an example of a natural phenomenon in which an observer’s the mental state can be fully described in mathematical terms analogous to the state vector that is being observed. This mathematical description of the o...