I have described generalized cofinite filters (including the “cofinite funcoid”). See the draft at http://www.mathematics21.org/binaries/addons.pdf
read moreDefine for posets with order $latex \sqsubseteq$: $latex \Phi_{\ast} f = \lambda b \in \mathfrak{B}: \bigsqcup \{ x \in \mathfrak{A} \mid f x \sqsubseteq b \}$; $latex \Phi^{\ast} f = \lambda b \in \mathfrak{A}: \bigsqcap \{ x \in \mathfrak{B} \mid f x…
read moreThe following is one of a few (possibly non-equivalent) definitions of products of funcoids: Definition Let $latex f$ be an indexed family of funcoids. Let $latex \mathcal{F}$ be a filter on $latex \mathrm{dom}\, f$. $latex a \mathrel{\left[ \prod^{[\mathcal{F}]} f \right]} b \Leftrightarrow…
read moreDefinition $latex a \mathrel{\left[ \prod^{(A 2)} f \right]} b \Leftrightarrow \exists M \in \mathrm{fin} \forall i \in (\mathrm{dom}\, f) \setminus M : \Pr^{\mathsf{RLD}}_i a \mathrel{[f_i]} \Pr^{\mathsf{RLD}}_i b$ for an indexed family $latex f$ of funcoids and atomic reloids $latex a$ and $latex…
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