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July 20, 2016 / porton

New easy theorem and its consequence

I’ve added to my book a new easy to prove theorem and its corollary:

Theorem If f is a (co-)complete funcoid then \mathrm{up}\, f is a filter.

Corollary

  1. If f is a (co-)complete funcoid then \mathrm{up}\, f = \mathrm{up} (\mathsf{RLD})_{\mathrm{out}} f.
  2. If f is a (co-)complete reloid then \mathrm{up}\, f = \mathrm{up}\, (\mathsf{FCD}) f.
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