Inspired by locale theory, we propose “pointfree convex geometry.” We introduce the notion of convexity algebra as pointfree convexity space. There are two notions of point for convexity algebra: one is chain-prime meet-complete filter and the other is maximal meet-complete filter. In this paper we show the following: (1) the former notion of point induces a dual equivalence between the categor...

The design argument is one of three main arguments for the existence of God; the others are the ontological argument and the cosmological argument. Unlike the ontological argument, the design argument and the cosmological argument are a posteriori. And whereas the cosmological argument can focus on any present event to get the ball rolling (arguing that it must trace back to a first cause, name...

For a poset P, let σ(P) and Γ(P) respectively denote the lattice of its Scott open subsets closed ordered by inclusion, set ΣP=(P,σ(P)). In this paper, we discuss lower Vietoris topology on give some sufficient conditions to make two topologies equal. We build an adjunction between σ(Γ(P)) prove that ΣP is core-compact iff ΣΓ(P) sober, locally compact σ(Γ(P))=υ(Γ(P)) (the topology). This answer...

Most automobile manufacturers and several technology companies are testing automated vehicles (AVs) on public roads. While automation of the driving task is expected to reduce crashes, there no consensus as how safe an AV must be before it can deployed. An should at least average driver, but national crash rates include drunk distracted driving, meaning that crashes rate somewhere between sober...