TITLE: Compact and quasi-compact
QUESTION [12 upvotes]: Why do algebraic geometers still use the term "quasi-compact" when they almost never deal with Hausdorff spaces?  They certainly use "local" rather than "quasi-local" (local = quasi-local + noetherian), so is there any reason other than historical contingency? 
Do algebraic geometers who do work in other fields still follow this convention when they write other papers?  If they do, do they write at the beginning of the paper something along the lines of "by compact, we mean quasi-compact and Hausdorff"?

REPLY [2 votes]: This is far from standard, but in my mind, when I'm doing algebraic geometry, "quasicompact" means "compact in the Zariski topology," and "compact" means "compact in the analytic topology" (or is not used at all if I'm not working over a topological field).  Thus, in principle, having explained that the terms were being used this way, one could write statements like  
"$\mathbb{A}^n_{\mathbb{C}}$ is quasicompact but not compact"
and
"Projective varieties are both compact and quasicompact."
But I would be very hesitant to do so, since I've never seen the terminology used this way so explicitly.