I am working through the book "Model Categories", by Mark Hovey, and have a doubt about a definition given there. At the beginning of page 50 we read:
Define a map $f:X\rightarrow Y$ to be a closed $T_1$ inclusion if $f$ is a closed inclusion and if every point not in $Y\backslash f(X)$ is closed in $Y$.
The bold "not" is the part troubling me. First of all, it seems strange in the phrasing of the definition. Personally I would have stated it as "if every point in $f(X)$". Second, a couple of pages later (p.52, corollary 2.4.6) he proves that some maps are closed $T_1$ inclusions by showing that every point in $Y\backslash f(X)$ is closed.
I am quite convinced that the "not" doesn't belong to the definition, but I would like a second opinion about that. Also, there is no correction about that definition in the errata at the end of the book. If this is effectively an error, what should I do? Try to contact AMS to tell them?