Namely, let <math>T</math> consist of the set of finite prefixes of the infinite sequences in <math>C</math>. Conversely, the body <math>[T]</math> of every tree <math>T</math> forms a closed set in this topology.
Frequently trees on [[Cartesian product]]s <math>X\times Y</math> are considered. In this case, by convention, thewe setconsider ofonly finitethe sequencessubset of members<math>T</math> of the product space, <math>(X\times Y)^{<\omega}</math>, iscontaining only sequences whose even elements come from <math>X</math> and odd elements come from <math>Y</math> (e.g., <math>\langle x_0,y_1,x_2,y_3\ldots,x_{2m}, y_{2m+1}\rangle</math>). Elements in this subspace are identified in the natural way with a subset of the product of two spaces of sequences, <math>X^{<\omega}\times Y^{<\omega}</math> (the subset offor memberswhich the length of the secondfirst productsequence foris whichequal bothto sequencesor have1 themore samethan the length of the second sequence).
In this way a tree <math>[T]</math> over the product spacewe may be considered as a subset ofidentify <math>[X^{<\omega}]\times [Y^{<\omega}]</math> with <math>[T]</math> for over the product space. We may then form the '''projection''' of <math>[T]</math>,
