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Values of a multifuncoid on atoms (Solved)
Conjecture
for every multifuncoid
of the form whose elements are atomic posets.
![$ 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 $](/files/tex/20328c795890b2a043f28afc705aecd5679f72d9.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
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.
Counter-example found
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