The enriched Vietoris monad on representable spaces

Employing a formal analogy between ordered sets and topological spaces, over the past years we have investigated a notion of cocompleteness for topological, approach and other kind of spaces. In this new context, the down-set monad becomes the filter monad, cocomplete ordered set translates to continuous lattice, distributivity means disconnectedness, and so on. Curiously, the dual(?) notion of completeness does not behave as the mirror image of the one of cocompleteness; and in this paper we have a closer look at complete spaces. In particular, we construct the “up-set monad” on representable spaces (in the sense of L. Nachbin for topological spaces, respectively C. Hermida for multicategories); we show that this monad is of Kock–Zöberlein type; we introduce and study a notion of weighted limit similar to the classical notion for enriched categories; and we describe the Kleisli category of our “up-set monad”. We emphasise that these generic categorical notions and results can be indeed connected to more “classical” topology: for topological spaces, the “up-set monad” becomes the lower Vietoris monad, and the statement “X   is totally cocomplete if and only if X^op$X^{\mathrm{op}}$ is totally complete” specialises to O. Wyler's characterisation of the algebras of the Vietoris monad on compact Hausdorff spaces as precisely the continuous lattices.     

A note on locally compact subsemigroups of compact groups

Semigroup Forum - An elementary proof is given for the fact that every locally compact subsemigroup of a compact topological group is a closed subgroup. A sample consequence is that every...     

Sterubin: Enantioresolution and Configurational Stability,Enantiomeric Purity in Nature,and Neuroprotective Activity in Vitro and in Vivo

Alzheimer′s disease (AD) is a neurological disorder with still no preventive or curative treatment. Flavonoids are phytochemicals with potential therapeutic value. Previous studies described the flavanone sterubin isolated from the Californian plant Eriodictyon californicum as a potent neuroprotectant in several in vitro assays. Herein, the resolution of synthetic racemic sterubin ( 1 ) into its two enantiomers, (R)- 1 and (S)- 1 , is described, which has been performed on a chiral chromatographic phase, and their stereochemical assignment online by HPLC-ECD coupling. (R)- 1 and (S)- 1 showed comparable neuroprotection in vitro with no significant differences. While the pure stereoisomers were configurationally stable in methanol, fast racemization was observed in the presence of culture medium. We also established the occurrence of extracted sterubin as its pure (S)-enantiomer. Moreover, the activity of sterubin ( 1 ) was investigated for the first time in vivo, in an AD mouse model. Sterubin ( 1 ) showed a significant positive impact on short- and long-term memory at low dosages.