关于可序性问题与区间拓扑
On the Orderability Problem and the Interval Topology
摘要：
LOTS（线性序拓扑空间，即具有由线性序生成的拓扑的空间）类包含许多重要的空间，如实数集、有理数集和序数。这样的空间具有丰富的拓扑性质，这些性质不一定是遗传的。可序性问题是一个关于拓扑空间是否存在线性序的重要问题，它生成与空间拓扑相等的拓扑，J.van Dalen和E. 1973年，沃特尔。在这篇文章中，我们首先调查的范达伦和瓦特尔的LOTS的表征的区间拓扑的作用，然后我们研究如何将这个模型扩展到传递关系，不一定是线性订单。
英文摘要：
The class of LOTS (linearly ordered topological spaces, i.e. spaces equipped with a topology generated by a linear order) contains many important spaces, like the set of real numbers, the set of rational numbers and the ordinals. Such spaces have rich topological properties, which are not necessarily hereditary. The Orderability Problem, a very important question on whether a topological space admits a linear order which generates a topology equal to the topology of the space, was given a general solution by J. van Dalen and E. Wattel, in 1973. In this article we first investigate the role of the interval topology in van Dalen's and Wattel's characterization of LOTS, and we then examine ways to extend this model to transitive relations that are not necessarily linear orders.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
