The relative interlevel set cohomology (RISC) is an invariant of real-valued continuous functions closely related to the Mayer--Vietoris pyramid introduced by Carlsson, de Silva, and Morozov. We provide a structure theorem, which applies to the RISC if it is pointwise finite dimensional (pfd) or, equivalently, $q$-tame. Moreover, we provide the notion of an interleaving for RISC and we show that it is stable in the sense that any space with two functions that are $\delta$-close induces a $\delta$-interleaving of the corresponding relative interlevel set cohomologies.

翻译：相对等级间组合共生学(RISC)是一个与卡尔松、德席尔瓦和莫罗佐夫引入的Mayer-Veaoris金字塔密切相关的实际价值连续功能的变量。 我们提供了一个结构理论,如果该结构理论是点数有限的维度(pfd)或等值的美元,则适用于RISC。 此外,我们为RISC提供了一种相互交错的概念,并且我们表明,具有两种功能即$delta$-close的任何空间都会引起相应的相对的相对水平间组合共生体的相互交错,这是稳定的。