We prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than theirs. JEL classific...

In the 1980's, remarkable advances were made by Ravenel, Hopkins, Devinatz, and Smith toward a global understanding of stable homotopy theory, showing that some major features arise "chromatically" from an interplay of periodic phenomena arranged in a hierarchy (see [20], [21], [28]). We would like very much to achieve a similar understanding in unstable homotopy theory and shall describe some ...

This paper will survey the various definitions of homology theories from the first Eilenberg-Mac Lane theories for group cohomology through the Cartan-Eilenberg attempt at a uniform (co-)homology theory in algebra, cotriple cohomology theories and the various acyclic models theorems that tied them all together (as much as was possible).

Consider a group G and an epimorphism u0 : G → Z inducing a splitting of G as a semidirect product ker(u0)oφ Z with ker(u0) a finitely generated free group and φ ∈ Out(ker(u0)) representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-Maclane 2–complex X equipped with a semiflow ψ, and inspired by McMullen’s T...

For a real central arrangement A, Salvetti introduced a construction of a finite complex Sal(A) which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement Ak−1, the Salvetti complex Sal(Ak−1) serves as a good combinatorial model for the homotopy type of the configuration space F (C, k) of k points in C, which is homotopy equivalent to th...

In this paper, for a valued field [Formula: see text] of arbitrary rank and an extension to relation between induced complete sequences abstract key polynomials MacLane-Vaquié chains is given.

An Eilenberg–like theorem is shown for algebras on a given monad. The main idea is to explore the approach given by Bojańczyk that defines, for a given monad T on a category D, pseudovarieties of T–algebras as classes of finite T–algebras closed under homomorphic images, subalgebras, and finite products. To define pseudovarieties of recognizable languages, which is the other main concept for an...