[see also: provide, offer, supply, furnish, afford, define, yield, imply, present, produce
The action of G is given by gf=......
The argument just given shows that......
This gives (1) and shows that......
We now give some applications of Theorem 3.
We give X the topology of uniform convergence on compact subsets of I.
Note that E can be given a complex structure by setting......
Suppose we are given an f of the form f=......
Given δ >0, we can find β such that......
This is certainly reasonable for Algorithm 3, given its simple loop structure.
A function given on G gives rise to an invariant function on G'.