Take the 2-minute tour ×  In some books the word "if" is used in
definitions and it is not clear if they actually mean "iff" (i.e
"if and only if"). I'd like to know if in mathematical
literature in general "if" in definitions means "iff".  For
example I am reading "Essential topology" and the following
definition is written:  "In a topological space T, a collection
B of open subsets of T is said to form a basis for the topology
on T if every open subset of T can be written as a union of sets
in B."  Should I assume the converse in such a case? Should I
assume that given a basis B for a topological space, every open
set can be written as a union of sets in B?  This is just an
example, I am not asking specifically about this sentence.
share|improve this question Your suspect is well-founded: in
mathematical literature always "if" in definitions means "iff" !
In fact "iff" theorems can be used as alternative definitions.
–  Tony Piccolo Nov 14 '13 at 9:17 The problem is that if "iff"
is true, then the "if" onl