We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially closed inhomogeneous cosmological models. The models, called the locally U(1)×U(1) symmetric models (or the generalized Gowdy models), are characterized by the existence of two commuting spatial local Killing vectors. For systematic investigations we first present a classification of possible ...

Creating ensembles of random but “realistic” topologies for complex systems is crucial for many tasks such as benchmark generation and algorithm analysis. In general, explanatory models are preferred to capture topologies of technological and biological complex systems, and some researchers claimed that it is largely impossible to capture any nontrivial network structure while ignoring domain-s...

This paper demonstrates the redundancies concerning the increasing popular ``soft set" approaches to general topologies. It is shown that there is a complement preserving isomorphism (preserving arbitrary $widetilde{bigcup}$ and arbitrary $widetilde{bigcap}$) between the lattice ($mathcal{ST}_E(X,E),widetilde{subset}$) of all soft sets on $X$ with the whole parameter set $E$ as domains and the ...