Аннотация:
In the last decade unexpectedly, some expected properties of thresholds
related to singularities and intersection properties were established.
In its turn, the acc for lc thresholds implies the uniform stability
of lc singularities and of the $\mathbb{R}$-complementary property. We present
a different approach to these and other results related to thresholds
based on the theory of complements. We start from an inversion of
both uniform stabilities. After that we explained how the inversion
can be applied to obtained some of already known and new results,
including but not only, lc and Fano index thresholds, lc indices, $a$, $\alpha$-
invariants.
