论文标题
无点的时空理论
Point-free theories of space and time
论文作者
论文摘要
该论文在基于区域的空间理论（RBT）的领域中，有时称为Mereotopology。 RBT是基于区域概念的一种无点的空间理论。它的起源可以追溯到怀特海，德拉古纳和塔斯基的一些思想，以建立空间理论，而无需使用观点。可以在\ cite {vak2007}中找到有关RBT和Mereotopology的更多信息。触点代数呈现RBT的代数配方，实际上给出了一些定期封闭的拓扑空间的布尔代数，并具有额外的接触关系。 \ cite {divak2006}对此理论进行了详尽的研究。本文作者引入的动态接触代数（DCA）\ cite {vak2014}（另请参见\ cite {vak2010，vak2012}），是由本作者介绍的，是对触点研究区域发生变化的触点的概括，并提出了对空间和空间的集成点的正式透明的正式透明。 DCA是特殊\ emph {Space模型}的抽象，也称为\ emph {snapshot}或\ emph {cinematographic}模型，纸张\ cite \ cite {vak2014}将预期的代表定理与此类模型有关。在本文中，我们引入了DCA的新版本，该版本是\ cite {vak2014}定义的简化版本，与\ cite {vak2012}相似。目的是将此版本用作DCA的代表性示例，并为此示例开发不仅是快照模型，还可以拓扑模型和预期的拓扑二元性理论，从某种意义上说明了布尔代数的众所周知的石材二重性。 DCA的抽象拓扑模型介绍了有关时空性质的新观点，并展示了如果我们从公制属性中抽象会发生什么。
The paper is in the field of Region Based Theory of Space (RBTS), sometimes called mereotopology. RBTS is a kind of point-free theory of space based on the notion of region. Its origin goes back to some ideas of Whitehead, De Laguna and Tarski to build the theory of space without the use of the notion of point. More information on RBTS and mereotopology can be found, for instance, in \cite{Vak2007}. Contact algebras present an algebraic formulation of RBTS and in fact give axiomatizations of the Boolean algebras of regular closed sets of some classes of topological spaces with an additional relation of contact. An exhaustive study of this theory is given in \cite{DiVak2006}. Dynamic contact algebra (DCA) \cite{Vak2014} (see also \cite{Vak2010,Vak2012}) introduced by the present author, is a generalization of contact algebra studying regions changing in time and presents a formal explication of Whitehead's ideas of integrated point-free theory of space and time. DCA is an abstraction of a special \emph{dynamic model of space}, called also \emph{snapshot} or \emph{cinematographic} model and the paper \cite{Vak2014} contains the expected representation theorem with respect to such models. In the present paper we introduce a new version of DCA which is a simplified version of the definition from \cite{Vak2014} and similar to that of \cite{Vak2012}. The aim is to use this version as a representative example of a DCA and to develop for this example not only the snapshot models but also topological models and the expected topological duality theory, generalizing in a certain sense the well known Stone duality for Boolean algebras. Abstract topological models of DCAs present a new view on the nature of space and time and show what happens if we are abstracting from their metric properties.
