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If I understand correctly, $\Delta$-complex on a space $X$ is defined to be a collection $\Delta(X)$ of cont. funtions $\sigma:\Delta^n\to X$ such that:

1) restriction of $\sigma$ to any face is in $\Delta(X)$

2) restriction of $\sigma$ to the interior is injective

3) $A \subseteq X$ is open if every $\sigma^{-1}(A)$ is open

Can anyone explain me how a singular complex $S(X)$ can be regarded as a $\Delta$-complex considering the condition (2)? I have read some books but I still don't get it. Thank you for your help.

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