Space architects and engineers alike tend to see spacecraft and space habitat design as an entirely new departure, disconnected from the Earth. However, at least for Space Architecture, there is a continuum of development since the earliest formalizations of terrestrial architecture. Moving out from 1-G, Space Architecture enables the continuum from 1-G to other gravity regimes. The history of ...

Abstract We introduce the notion of an introverted Boolean algebra $\mathcal{B}$ closed-and-open subsets a topological group G, show that associated Stone space $(\nu_{\mathcal{B}} \nu_{\mathcal{B}})$ is totally disconnected semigroup compactification G and every takes this form. identify study universal compactification, semitopological G. Our main results are obtained independently Gelfand th...

For any non-totally disconnected Polish space, there is a family of c = 2א0 many Wadge incomparable finite level Borel subsets. If the space is additionally locally compact or locally connected, there is a family of 2 many Wadge incomparable subsets. In this note, we study the Wadge order for Polish spaces which are not totally disconnected. For a fixed Polish space, the Wadge order for the spa...

A general method for solving the Cosmological Einstein’s Field Equations (EFE) in vacuum is presented, and is applied to the Bianchi Type III vacuum cosmology. As a result, the entire space of solutions for this model is found. This space is composed of two distinct, disconnected ,three-parameter families. Both of them admit four Killing vector Fields and no homothetic vector. One family repres...

We define E-theory for separable C∗-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite approximations to this space. We obtain effective criteria for determining the invertibility of E-theory elements over possibly infinite-dimensional spaces. Fu...

We argue in a quantitative way that the unitarity principle of quantum field theory together with information bound on correlation functions is tension space which made out disconnected patches at microscopic scales.

Q × ́ and induces a metric topology in this group. We show that the completion of this metric space is a Banach space over the field R of real numbers. We further show that this Banach space is isometrically isomorphic to a co-dimension one subspace of L(Y,B, λ), where Y is a certain totally disconnected, locally compact space, B is the σ-algebra of Borel subsets of Y , and λ is a certain measur...

The logical theory of branching space-times (Belnap, Synthese 1992), which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from the discussion of space-time theories in the philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time” (2008). This paper identifies the differ...

One of the striking initial applications of the Seiberg-Witten invariants was to give new obstructions to the existence of Riemannian metrics of positive scalar curvature on 4– manifolds. The vanishing of the Seiberg–Witten invariants of a manifold admitting such a metric may be viewed as a non-linear generalization of the classic conditions [16, 15, 21] derived from the Dirac operator. If a ma...