"The operation is normal iff it's both monotone and continuous" -- which math area studies operation? I just read Enderton's "Elements of Set Theory" to have a basic understanding of sets (btw it's a great book). One line of it says: "the operation is normal iff it's both monotone and continuous."
I'm wondering, the terms, normal, monotone, continuous, seems not come from the thin air. are these some common terms in a specific math area that studies operation/operator ? is it algebra? 

The part of Enderton you quote is his own definition of the word “normal” for a particular thing he calls an “operation.” “Normal” is perhaps the most overused word in all of mathematics, but I'm not a set theorist, so I can’t say where his use of it was inspired. It appears in every subfield of mathematics with widely different meanings.
Enderton’s “operations” are basically functions. He doesn’t call them functions only because their domain (all ordinals) is not a set. The word “monotone” comes from analysis mostly, and “continuous” comes from analysis or topology. 
All fields of mathematics overlap, but if you want to find out more about monotone, continuous things, a book on analysis, and perhaps a gentle one on topology as well, would be good places to start.
