Extension of zero-dimensional hyperbolic sets to locally maximal ones

It is proved that in any neighbourhood of a zero-dimensional hyperbolic set $F$ (hyperbolic sets are assumed to be compact) there is a locally maximal set $F_1\supset F$. In the proof, several already known or simple results are used, whose statements are given as separate assertions. The main theorem is compared with known related results, whose statements are also presented. (For example, it is known that the existence of $F_1$ is not guaranteed for $F$ of positive dimension.)
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