Let $latex \mathfrak{A}$ be an indexed family of sets.

Products are $latex \prod A$ for $latex A \in \prod \mathfrak{A}$.

Hyperfuncoids are filters $latex \mathfrak{F} \Gamma$ on the lattice $latex \Gamma$ of all finite unions of products.

Is $latex \bigsqcap^{\mathsf{FCD}}$ a bijection from hyperfuncoids $latex \mathfrak{F} \Gamma$ to:

  1. prestaroids on $latex \mathfrak{A}$;
  2. staroids on $latex \mathfrak{A}$;
  3. completary staroids on $latex \mathfrak{A}$?

If yes, is $latex \mathrm{up}^{\Gamma}$ defining the inverse bijection?

If not, characterize the image of the function $latex \bigsqcap^{\mathsf{FCD}}$ defined on $latex \mathfrak{F} \Gamma$.

1 thought on “What are hyperfuncoids isomorphic to?

  1. Consider also the variant of this problem with the set $latex \Gamma$ replaced with the set $latex \Gamma^{\ast}$ of complements of elements of the set $latex \Gamma$.

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