We propose a new way to hide large extra dimensions without invoking branes, based on Lorentzviolating tensor fields with expectation values along the extra directions. We investigate the case of a single vector aether field on a compact circle. In such a background, interactions of other fields with the aether can lead to modified dispersion relations, increasing the mass of the Kaluza-Klein e...

The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

A bijective correspondence between strong inclusions and compactifications in the setting of σ-frames is presented. The category of uniform σ-frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the σ-frame consisting of its uniform cozero part, and consequently, any compactificat...

We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out that (i) the Bohr compactification of an ultraproduct of finite simple groups is trivial, and (ii) the “definable” Bohr compactification of any pseudofinite group G, relative to an ambient nonstandard model of set theory in which it...

We construct a new compactification of the moduli space Hg of smooth hyperelliptic curves of genus g. We compare our compactification with other well-known remarkable compactifications of Hg.

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon. Connectedness and compactness are two fundamental topological properties. A natural question is whether a given space admits a connected (Hausdorff) compactification. This question has been st...