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    S(S(f)) = S(f) for reloids
See Algebraic General Topology, especially Connectedness of funcoids and reloids for definitions of used concepts.
Bibliography
*Victor Porton. Algebraic General Topology
* indicates original appearance(s) of problem.
 
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 CSI of Charles University
Mistake fixed
There were a big mistake in http://www.mathematics21.org/binaries/connectedness.pdf where are defined some of the concepts used by this open problem. I have rewritten the article, not it should be OK.
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Victor Porton - http://www.mathematics21.org