Using the Relational Model to Capture Topological Information of Spaces
Using the Relational Model to Capture Topological Information of Spaces
复制标题
使用关系模型捕获空间的拓扑信息
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
N. Paul
中科院分区：
文献类型：
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作者：
P. Bradley;N. Paul
出于对拓扑如何可能是一个有用的基础建设信息建模的研究，链复杂和链复杂态射的概念的关系数据库版本的定义和用于存储CW-复杂和它们的态射，因此建设项目的实例和不同的意见，到关系数据库。在许多情况下，这可以在不丢失拓扑信息的情况下完成。二元关系和亚历山德罗夫空间的集合之间的范畴的等价性被证明，并用于将关系复合体纳入更一般的设置拓扑数据库。对于后者，通过将通常的关系代数运算符转换为拓扑结构来定义关系查询语言的拓扑版本。最后，证明了这样一个拓扑形式的关系代数在一般情况下必须能够计算一个关系的传递闭包。
Motivated by research on how topology may be a helpful foundation for building information modelling, a relational database version of the notions of chain complex and chain complex morphism is defined and used for storing cw-complexes and their morphisms, hence instances of building projects and different views upon them, into relational databases. In many cases, this can be done without loss of topological information. The equivalence of categories between sets with binary relations and Alexandrov spaces is proven and used to incorporate the relational complexes into the more general setting of topological databases. For the latter, a topological version of a relational query language is defined by transferring the usual relational algebra operators into topological constructions. In the end, it is proven that such a topological version of relational algebra in general must be able to compute the transitive closure of a relation.