Skip to content
November 4, 2016 / porton

A new kind of product of funcoids

The following is one of a few (possibly non-equivalent) definitions of products of funcoids:

Definition Let f be an indexed family of funcoids. Let \mathcal{F} be a filter on \mathrm{dom}\, f. a \mathrel{\left[ \prod^{[\mathcal{F}]} f \right]} b \Leftrightarrow \exists N \in \mathcal{F} \forall i \in N : \mathrm{Pr}^{\mathsf{RLD}}_i\, a \mathrel{[f_i]} \mathrm{Pr}^{\mathsf{RLD}}_i\, b.
for atomic reloids a and b.

Today I have proved that this really defines a funcoid. Currently the proof is present in draft of the second volume of my book,

A probably especially interesting case is if \mathcal{F} is the cofinite filter. In this way we get something similar to Tychonoff product of topological spaces.

This may possibly have some use in study of compact funcoids.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: