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Several ways to apply a (multivalued) multiargument function to a family of filters ★★★

Author(s): Porton

Problem   Let $ \mathcal{X} $ be an indexed family of filters on sets. Which of the below items are always pairwise equal?

1. The funcoid corresponding to this function (considered as a single argument function on indexed families) applied to the reloidal product of filters $ \mathcal{X} $.

2. The funcoid corresponding to this function (considered as a single argument function on indexed families) applied to the starred reloidal product of filters $ \mathcal{X} $.

3. $ \bigcap_{F\in\operatorname{up}^{\mathrm{FCD}}\prod^{\mathrm{Strd}}\mathcal{X}}\langle f \rangle F $.

Keywords: funcoid; function; multifuncoid; staroid

Posted by porton
updated January 15th, 2020
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