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March 16, 2016 / porton

I’ve partially proved a conjecture

The following is a conjecture:

Conjecture The set of pointfree funcoids between two boolean lattices is itself a boolean lattice.

Today I have proved its special case:

Theorem The set of pointfree funcoids between a complete boolean lattice and an atomistic boolean lattice is itself a boolean lattice.

It is a very weird theorem because of its asymmetric conditions.

My proof (preluded with some special cases for better readability) is presented in this PDF file. Note that in the future I am going to more it from this file to my book.

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