# Acyclicity is product-closed

This article gives the statement, and possibly proof, of a topological space property (i.e., acyclic space) satisfying a topological space metaproperty (i.e., product-closed property of topological spaces)
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## Statement

### For two spaces

Suppose $X_1$ and $X_2$ are topological spaces that are both acyclic spaces. Then, the product space $X_1 \times X_2$, endowed with the product topology, is also an Acyclic space (?).

### For finitely many spaces

Suppose $X_1, X_2, \dots, X_n$ are topological spaces that are all acyclic spaces. Then, the product space $X_1 \times X_2 \times \dots \times X_n$, endowed with the product topology, is also an acyclic space.

### For an arbitrary number of spaces

Suppose $X_i, i \in I$, are topological spaces that are all acyclic spaces. Then, the product space $\prod_{i \in I} X_i$, endowed with the product topology, is also an acyclic space.