Under this hypothesis, the notions of weak and strong limit cardinals coincide.

This notion coincides with the concepts frame and locale.

The two notions coincide only when all error terms (not shown in the diagram) are statistically uncorrelated.

Every paracompact space is a-paracompact, and in regular spaces the two notions coincide.

For fractals that occur in nature, the two notions coincide.

In other words, for Fredholm operators, the two notions of index coincide.

Note that the two notions of boundedness coincide for locally convex spaces.

If I is the zero ideal and A is a field, these notions coincide with 0-smooth etc. as defined above.

The notion of a semi-Thue system essentially coincides with the presentation of a monoid.

When the base is the field of complex numbers, these notions coincide with the previous definition.