We investigate the role of topology in space-time scaling limit quantum quench dynamics, where both time and system size tend to infinity at a constant ratio. There, while standard topological characterization relying on local unitary transformations becomes ill defined, we show how different dynamical notion naturally arises through winding number encoding linear response Berry phase magnetic ...

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I als show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail pr...

Eisenbud and Harris introduced the theory of limit linear series, and constructed a space parametrizing their limit linear series. Recently, Osserman introduced a new space which compactifies the Eisenbud-Harris construction. In the Eisenbud-Harris space, the set of refined limit linear series is always dense on a general reducible curve. Osserman asks when the same is true for his space. In th...

Cyberspace and its impact as the main competitor of real space in various aspects is considered and have been studied by many thinkers and theorists. For various reasons (political, social, cultural, etc.) it is lead to the presence of people, especially young people in virtual space, as all borders crossed the behavior and influence actions of people. According to the increasing importance and...

O. Wyler [Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.] has given a Stone-Cech compactification for limit spaces. However, his is not necessarily an embedding. Here, it is shown that any Hausdorff limit space (X, t) can be embedded as a dense subspace of a compact, Hausdorff, limit space (Xi, ri) with the following property: any continuous function from (X, t) into a compact, Hau...