论文标题
真实线的范围
The spectrum of the real line
论文作者
论文摘要
通过研究真实线的持久性模块的研究，我们研究了完全有序集合的线性表示类别。我们表明，该类别在本地相干，我们将不可分解的外观对象分类为同构。这些类构成了频谱，我们表明对有序空间是同构的。此外，由于光谱类别被证明是离散的，光谱参数将所有注射对象参数。 最后，对于真实行的情况，我们表明这种拓扑结合了与持久性同源性相互交织距离引起的拓扑结构。
Motivated by the study of persistence modules over the real line, we investigate the category of linear representations of a totally ordered set. We show that this category is locally coherent and we classify the indecomposable injective objects up to isomorphism. These classes form the spectrum, which we show to be homeomorphic to an ordered space. Moreover, as the spectral category turns out to be discrete, the spectrum parametrises all injective objects. Finally, for the case of the real line we show that this topology refines the topology induced by the interleaving distance, which is known from persistence homology.
