= Cylinder set
{title2=$\pi_F^{-1}(A)$}
A cylinder set in a product of spaces restricts a finite collection of coordinates $F$ and leaves all other coordinates free. It has the form $\pi_F^{-1}(A)$, where $\pi_F$ is the coordinate projection onto the finite subproduct. Taking $A$ to be a product of <open sets> gives the basic open cylinders for the <product topology>. In a finite-alphabet <full shift>, specifying exact letters at finitely many coordinates gives a <clopen set>.
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