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August 2, 2016 / porton

Filter rebase generalized

I have re-defined filter rebase. Now it is defined for arbitrary filter \mathcal{A} on some set \mathrm{Base}(\mathcal{A}) and arbitrary set A.

The new definition is: \mathcal{A}\div A = \{ X\in\mathscr{P}A \mid \exists Y\in\mathcal{A}: Y\cap A\subseteq X \}.

It is shown that for the special case of \forall X\in\mathcal{A}:X\subseteq A the new definition is equal to the old definition that is \mathcal{A}\div A = \{ X\in\mathscr{P}A \mid \exists Y\in\mathcal{A}: Y\subseteq X \}.

See my book (updated), chapter “Orderings of filters in terms of reloids”, for details.

The new definition is useful for studying restrictions and embeddings of funcoids and reloids.

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