n-movable compacta and ANR-systems

Concurrent semantics for timed distributed systems Livrable du projet ANR ImpRo (ANR-2010-BLAN-0317)

Several formalisms to model distributed real-time systems coexist in the literature. This naturally induces a need to compare their expressiveness and to translate models from one formalism to another when possible. The first formal comparisons of the expressiveness of these models focused on the preservation of the sequential behavior of the models, using notions like timed language equivalenc...

Sparse Days and ANR SOLSTICE

THE EXISTENCE OF n-SHAPE THEORY FOR ARBITRARY COMPACTA

Shape theory is an extension of homotopy theory which uses the idea of homotopy in its conception. By comparison, the theory of n-shape, which heretofore only has been defined for metrizable compacta, has as its basic notion that of n-homotopy instead of homotopy. We shall demonstrate that the theory of n-shape extends to the class of all Hausdorff compacta.

Noetherian Types of Homogeneous Compacta and Dyadic Compacta

The Noetherian type of a space is the least κ such that it has a base that is κ-like with respect to reverse inclusion. Just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Noetherian type and related cardinal functions. We prove these and many other results about these cardinal functions. For example, every homogeneous dyadic compactu...

Aronszajn Compacta ∗

We consider a class of compacta X such that the maps from X onto metric compacta define an Aronszajn tree of closed subsets of X.