Let (X,d) be a compact metric space and f a continuous transformation on X. f has the specification if one can always find a single orbit to interpolate between different pieces of orbits, up to a pre-assigned error. We call the map \mu to h_{\mu}(f) (Kolmogorov-Sinai entropy)the entropy map . Does specification implies that entropy map is upper semicontinuous?

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notupper semi-continuous, and see if you can find something from that list with specification. – Vaughn Climenhaga Jun 16 '11 at 11:45