We define the bigraded persistent homology modules and the bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove the stability theorem for the bigraded persistent double homology modules and barcodes.

翻译：我们利用与X的Vietoris-Rips滤流形相关联的矩角复形的普通同调与双重同调，定义了有限伪度量空间X的大分次持续同调模与大分次条码。我们证明了大分次持续双重同调模与条码的稳定性定理。