We call a nitely complete category algebraically coherent if the change-ofbase functors of its bration of points are coherent, which means that they preserve nite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdor algebras over a ...

In 1998, J. Previte developed a framework for studying the dynamics of iterated replacements of certain vertices in a finite graph G by a finite graph H (see [3]). He showed that, except for special cases, the sequence of graphs formed by iterating vertex replacements converges in the Gromov-Hausdor¤ metric. In this paper we prove that the topological dimension of these limit spaces is one. We ...

Let A be a C*-algebra with identity and supposeA has real rank 0. Suppose a complex-valued function is holomorphic and bounded on the intersection of the open unit ball of A and the identity component of the set of invertible elements of A. We show that then the function has a holomorphic extension to the entire open unit ball of A. Further, we show that this does not hold when A = C(S), where ...

An earlier result states that, on the surface of a convex polyhedron with vertices endowed with its intrinsic metric, a point cannot have more than antipodes (farthest points). In this paper we produce examples of polyhedra with vertices, on which some suitable point admits exactly antipodes. We also proved that, for any positive number 1, there exist (in the closure of the set of these polyhed...

This paper proposes a simple, fairly general, test for global identi cation of unconditional moment restrictions implied from pointidenti ed conditional moment restrictions. The test is based on the Hausdor distance between an estimator that is consistent even under global identi cation failure of the unconditional moment restrictions, and an estimator of the identi ed set of the unconditional ...

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

The implicit function theorem implies that the zero set of a smooth function, the set where the function vanishes, is a smooth hypersurface away from the critical zero set. Hence to study zero sets it is important to understand the structure of the critical zero sets. For solutions of the second order elliptic equations the critical zero sets represent the singular parts of zero sets. They have...

A domain representation of a topological space X is a function usually a quotient map from a subset of a domain onto X Several di erent classes of domain representations are introduced and studied It is investigated when it is possible to build domain representations from existing ones It is for example discussed whether there exists a natural way to build a domain representation of a product o...