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March 26, 2017 porton

A base of a funcoid which is not a filter base

The converse of this theorem does not hold.

Counterexample: Take $S = \mathrm{up}\, \mathrm{id}^{\mathsf{FCD}}_{\Omega}$ . We know that $S$ is not a filter base. But it is trivial to prove that $S$ is a base of the funcoid $\mathrm{id}^{\mathsf{FCD}}_{\Omega}$ .

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