Globalization of Confluent Partial Actions on Topological and Metric Spaces

We generalize Exel's notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably well-behaved systems of generators and relations, we employ classical rewriting theory in order to describe the universal induced global action on an extended set. This universal action can be lifted to the setting of topological spaces and continuous maps, as well as to that of metric spaces and non-expansive maps. Well-known constructions such as Shimrat's homogeneous extension are special cases of this construction. We investigate various properties of the arising spaces in relation to the original space; in particular, we prove embedding theorems and preservation properties concerning separation axioms and dimension. These results imply that every normal (metric) space can be embedded into a normal (metrically) ultrahomogeneous space of the same dimension and cardinality.Comment: New presentation of material on rewritin

One-Point Suspensions and Wreath Products of Polytopes and Spheres

It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with various interesting combinatorial and topological properties. In particular, infinitely many non-PL spheres as well as contractible simplicial complexes with a vertex-transitive group of automorphisms can be obtained in this way.Comment: 17 pages, 8 figure

Lumpy Investment and State-Dependent Pricing in General Equilibrium

The lumpy nature of plant-level investment is generally not taken into account in the context of monetary theory (see, e.g., Christiano et al. 2005 and Woodford 2005). We formulate a generalized (S,s) pricing and investment model which is empirically more plausible along that dimension. Surprisingly, our main result shows that the presence of lumpy investment casts doubt on the ability of sticky prices to imply a quantitatively relevant monetary transmission mechanism.Lumpy investment, Sticky prices

Four quotient set gems

Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the Monthly, despite its intense coverage of quotient sets over the years.Comment: 9 pages, to appear in the American Mathematical Monthl

Experiences with alloy in undergraduate formal methods

At the core of all engineering endeavors is the modeling of proposed system designs and the use of these models to determine system properties. While some models are physical, the vast majority use mathematics to both describe and analyze the consequences of design decisions. In the case of traditional engineering disciplines, most models are based on continuous mathematics, e.g., calculus and differential equations. The situation is quite different in software engineering, however, where the applicable models are more likely to be drawn from discrete mathematics, logic, and set theory. The term of art for such modeling approaches is formal methods