拓扑空间和度量空间上合流部分作用的整体化
Globalization of Confluent Partial Actions on Topological and Metric Spaces
摘要：
将Exel的部分群作用概念推广到幺半群.对于部分幺半群的行动，可以通过适当的行为良好的系统的发电机和关系，我们采用经典的重写理论，以描述普遍诱导的整体行动的扩展集。这个普适作用可以推广到拓扑空间和连续映射，也可以推广到度量空间和非扩张映射。著名的构造，例如Shimrat的齐次扩张，是该构造的特例。我们调查的各种性质的产生空间的原始空间，特别是，我们证明了嵌入定理和保存有关分离公理和尺寸的属性。这些结果意味着每个正规（度量）空间都可以嵌入到具有相同维数和基数的正规（度量）超齐性空间中。
英文摘要：
We generalize Exel's notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably well-behaved systems of generators and relations, we employ classical rewriting theory in order to describe the universal induced global action on an extended set. This universal action can be lifted to the setting of topological spaces and continuous maps, as well as to that of metric spaces and non-expansive maps. Well-known constructions such as Shimrat's homogeneous extension are special cases of this construction. We investigate various properties of the arising spaces in relation to the original space; in particular, we prove embedding theorems and preservation properties concerning separation axioms and dimension. These results imply that every normal (metric) space can be embedded into a normal (metrically) ultrahomogeneous space of the same dimension and cardinality.
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