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March 22, 2016 / porton

A new negative result in pointfree topology

I have proved the following negative result:

Theorem \mathsf{pFCD} (\mathfrak{A};\mathfrak{A}) is not boolean if \mathfrak{A} is a non-atomic boolean lattice.

The theorem is presented in this file.

\mathsf{pFCD}(\mathfrak{A};\mathfrak{B}) denotes the set of pointfree funcoids from a poset \mathfrak{A} to a poset \mathfrak{B} (see my free ebook).

The theorem and its proof were modeled after theorem 3.8 in this article (December 1979) by Zahava Shmuely.

It would be probably interesting to a find a common generalization of my theorem and the original Zahava Shmuely’s one.

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