We write K(Q) for K to make the dependence on Q explicit.
This module is denoted by H(X), or H(X,R) if we want to make explicit the coefficient ring.
For simplicity, we suppress the explicit dependence on x in the notation.
We shall proceed without making explicit distinctions between the two types of convergence.
Throughout what follows, we shall freely use without explicit mention the elementary fact that......
An explicit example is two planes through the origin.
Here is a more explicit statement of what the theorem asserts.