# 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.