[see also: all, any, each, arbitrary
To every F there corresponds a unique......
For every g in X <not in X> there exists an X...... [ But: for all f and g, for any two maps f and g; every is followed by a singular verb.]
Every invariant subspace is of the form......
[Do not write: “Every subspace is not of the form......” if you mean: No subspace is of the form......; every has to be followed by an affirmative statement.]
However, not every ring enjoys the stronger property of being bounded.
Every possible such sequence gives rise to......
The generally accepted point of view in this domain of science seems to be changing every few years.