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Inverse limits need not exist in the category of compact spaces and Feller kernels: A counterexample. (English) Zbl 0585.46062
It is shown that in the category with compact spaces as objects and Feller kernels as morphisms inverse limits need not exist. A result by C. L. Scheffer in C. R. Acad. Sci., Paris, Sér. I 272, 1198-1201 (1971; Zbl 0216.210), is thus disproved. The counterexample is based on the fact that a Poulsen simplex may be represented as the decreasing intersection of Bauer simplexes.
46M40 Inductive and projective limits in functional analysis
46A55 Convex sets in topological linear spaces; Choquet theory
47D07 Markov semigroups and applications to diffusion processes
60J99 Markov processes
Zbl 0216.210
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