Conference on the Frames and Spaces of Ordered Algebraic Structures

本次会议于2006年3月9日至11日在佛罗里达大学举行。 它被称为Ord 06/UF本次会议是在1998年发起的一系列的第九次; thesconference已涉及有序代数结构的某些方面。Ord 06/UF专注于框架理论在主题中的作用。Ord 06/UF，像它的前辈在该系列，汇集了25至30名数学家从不同的地方地球仪，包括研究生和那些谁最近获得了博士学位。计划出版Ord 06/UF的会议记录。只要有数学家的学术培训，研究和教学都试图抽象作为理解具体和特殊的一种手段。因此，数的算术性质被抽象到群和环的理论中，这些代数结构被发明来“解释”为什么真实的数会有这样的行为。另一派研究人员抓住了空间中数或点之间距离的几何概念，发展了拓扑空间的抽象概念，它建立了一种不测量距离的邻近感。在这两种概括中，目的始终是通过抽象行为来捕捉更大的现象目录，而不是创造一个促使抽象的实例的深奥复制品。在这种精神下，有序代数结构主义者采用了真实的数的自然排序，以及它的算术和拓扑方面，并发展了格序群和环。Ord 06/UF的贡献者，广泛地说，有一个共同的兴趣，即如何最好地描述一个格序群的函数，这些函数的大部分值都是真实的数，并且该结构的特征被转移到函数的代数中。在这种性质的追踪中，拓扑空间及其对框架的推广越来越发挥重要作用。特别是代数框架的概念具有双重身份，使一个概念能够同时捕捉拓扑和算术性质，而且，一组性质如何影响另一组性质。

This conference is held at the University of Florida, from March 9th through the 11th, 2006. It is referred to as Ord06/UFThis conference is the ninth in a series initiated in 1998; theseconferences have involved some aspect of Ordered Algebraic Structures. Ord06/UF concentrates on the role of frame theory in the subject. Ord06/UF, like its predecessors in the series, brings together 25 to 30 mathematicians from various parts of the globe, including graduate students and those who have recently received their PhD degrees. A published proceedings of Ord06/UF is planned. For as long as there has been academic training of mathematicians, research and instruction have sought to abstract as a means towards understanding of the concrete and the particular. Thus, the arithmetical properties of numbers became abstracted to the theory of groups and rings, these being algebraic constructs invented to ``explain'' why the real numbers, for example, behave the way they do. Another school of researchers seized upon the geometric notion of distance between numbers or points in space to develop the abstract concept of a topological space, which establishesa sense of proximity without measurement of distance. In both of these generalizations the aim has consistently been to capture a greater catalogue of phenomena by the act of abstraction, and not to create an esoteric replica of the instance that prompted the abstraction. In this spirit the Ordered Algebraic Structurist has taken the natural ordering of real numbers, together with its arithmetical and topological aspects, and developed the lattice-ordered group and ring. The contributors to Ord06/UF, broadly, have in common an interest in how a lattice-ordered group may best be described by functions which take on most of their values in the real numbers, and in which features of the construct are carried over to the algebra of functions. In this tracking of properties, topological spaces and their generalization to frames have increasingly played an important role. The notion of an algebraic frame, in particular, has a dual identity, enabling one to simultaneously capture topological and arithmetical properties, and, moreover, how one set of properties influences the other.