Computability of the causal boundary by using isocausality

Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the present paper, we consider the notion of isocausality given by Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out isocausal comparisons with standard stationary spacetimes. As a consequence, the qualitative behavior of the c-boundary (at the three levels: point set, chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the inclusion of Figure

On localizations of quasi-simple groups with given countable center

A group homomorphism $i: H \to G$ is a localization of $H$ if for every homomorphism $\varphi: H\rightarrow G$ there exists a unique endomorphism $\psi: G\rightarrow G$, such that $i \psi=\varphi$ (maps are acting on the right). G\"{o}bel and Trlifaj asked in \cite[Problem 30.4(4), p. 831]{GT12} which abelian groups are centers of localizations of simple groups. Approaching this question we show that every countable abelian group is indeed the center of some localization of a quasi-simple group, i.e. a central extension of a simple group. The proof uses Obraztsov and Ol'shanskii's construction of infinite simple groups with a special subgroup lattice and also extensions of results on localizations of finite simple groups by the second author and Scherer, Th\'{e}venaz and Viruel.Comment: 21 page

Different invasibility of permanent and temporary waterbodies in a semiarid Mediterranean Island

Nonindigenous species (NIS) represent a threat to aquatic biodiversity worldwide. However, freshwater ecosystems in drylands are potentially more prone to biological invasions than those located in temperate regions because of the higher number of artificial waterbodies generally occurring in these areas, which might act as invasion hubs for NIS. We review the available information about NIS in Sicilian waterbodies, discuss the role exerted by artificial lakes and ponds in facilitating the establishment of NIS in arid and semiarid areas, and compare the invasibility of permanent and temporary waterbodies in drylands. Artificial waterbodies increase the target-area effect for dispersers and provide a hospitable environment for NIS because of their recent origin and the lack of efficient biological filters against newcomers, thus acting as bridgeheads and invasion hubs favouring invasive species. Finally, we propose actions to attenuate the threats caused by NIS to the sensitive native biota of aquatic ecosystems in drylands

Generators and closed classes of groups

We show that in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. We also establish several new relations between singly-generated closed classes.Comment: 22 page