# topological space of Wang Tile

When trying to reprove a theorem in Wang tile: An established proof in Wang Tile which I doubt , a few notions are provided which I would like to seek for more information:

For a given set of blocks A (all 1x1, 2x2, 3x3 ... blocks), a solution T to A satisfies that: in T all occurring finite blocks belong A.

One notion mentioned is that:

"Note that the set of solutions of a set $A$ is a closed set (with respect to the product topology): every tiling that is not a solution of $A$ has an occurrence of a finite pattern $p$ not in $A$, and the cylinder set around $p$ (the set of all tilings with pattern $p$ on the same position) is an open set consisting only of tilings that are not solutions of $A$."

The above idea is well rationalized.

While topological knowledge in Wang Tile seems to be an interesting topics. Does anyone have some reference on this topic?

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Look up the product topology - especially the product topology of finite spaces. You might look at a book on symbolic dynamics. –  Anthony Quas May 28 at 18:05