Values of a multifuncoid on atoms (Solved)

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Posted	by:	porton
	on:	September 17th, 2012

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Porton, Victor

Conjecture $L \in \mathrel{\left[ f \right]} \Rightarrow \mathrel{\left[ f \right]} \cap \prod_{i \in \operatorname{dom} \mathfrak{A}} \operatorname{atoms} L_i \neq \emptyset$ for every multifuncoid $f$ of the form whose elements are atomic posets.

See Algebraic General Topology, especially the theory of multifuncoids for definitions of used concepts.

See this my online article and in this MathOverflow answer for a counter-example.

Bibliography

*Victor Porton. Algebraic General Topology

* indicates original appearance(s) of problem.

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Counter-example found

On December 13th, 2014 porton says:

Earlier I claimed that the conjecture is proved. There was an error in my proof. Now I propose a counter-example.

Victor Porton - http://www.mathematics21.org