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## Main Question or Discussion Point

**definitions using "if" instead of "iff"**

when a mathematical definition uses the word "if", can we assume that it also means "iff"?

for example, here's a defintion straight from a book:

definition: a bijection f is a homeomorphism if f and its inverse are continuous.

so this definition means that

(f and its inverse are continuous) implies (f is a homeomorphism).

but the converse is not stated because the definition uses "if" instead of "iff". So literally, based on the above definition, if f is a homeomorphism, then we cannot conclude that f and its inverse are continuous. but that's not true. what's going on? does "if" mean "iff" when we see "if" in a definition?

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