The converse of this theorem does not hold.
Counterexample: Take . We know that
is not a filter base. But it is trivial to prove that
is a base of the funcoid
.
Math Research of Victor Porton
Algebraic General Topology, Axiomatic Theory of Formulas, (generalized) limit of arbitrary function
The converse of this theorem does not hold.
Counterexample: Take . We know that
is not a filter base. But it is trivial to prove that
is a base of the funcoid
.