Angelaki, Volume 16, Issue 1, Page 1-3, 01Mar2011.

This paper uses the locale theory approach to topology. Two descriptions are given of all locale limits, the first description using suplattice constructions and the second preframe constructions. The symmetries between these two approaches to locale theory are explored. Given an informal assumption that open locale maps are parallel to proper maps we argue that various pairs of locale theory results are ‘parallel’, that is, identical in structure but prove facts about proper maps on one side of the pair and (...) about open maps on the other. The pairs of results are: pullback stability of proper/open maps, regularity of the category of compact Hausdorff/discrete locales, and theorems on information systems. Some remarks are included on a possible formalization of this parallel as a duality. (shrink)

This paper examines the apparent contradictions between the use of the fragmented close-up in Fernand Léger's film Ballet mécanique and his depiction of the cohesive face in his painting in the early 1920s. I argue that this paradox stems from Léger's seeing, in certain pre-war movements whose aesthetics were premised on fragmentation, an endorsement of the supreme value of technology and modernity to the human subject, and of the suborning of that subject to industrial modernity, with all the catastrophic human (...) consequences that were then witnessed in the First World War. These “aesthetics of fragmentation” are then compared and contrasted with Purism's post-war reconciliation of “man” as a cohesive being, achieved through its conservative revision of modernist aesthetics. This critique is effected through the “portmanteau” of Ballet mécanique, which is effectively an assemblage of different pre-war modernist aesthetics contrasted with Purist depictions of cohesive form. (shrink)