Lee Rudolph wrote: > "Gene Ward Smith" <email@example.com> writes: > > >>On the other hand, sometimes painful issues do arise. The Whitehead >>problem, whether or not Ext^1(A, Z)=0 for A an abelian group entails >>that A is free, was a shocker to algebraists, you may recall. > > > And yet (perhaps tellingly, perhaps not) Osofsky's result wasn't--as > far as I've ever been able to see--considered to be a shocker, or > even more than a mild "ho hum", among topologists (at least, geometric > topologists), though Whitehead (J.H.C.) brought up the problem for > topological reasons in a topological context. As a matter of fact > and practice, (geometric) topologists never (or hardly ever) need > to deal with spaces so "big" that that independence result makes any > difference to them. Similar comments apply, less strongly, to similar > independence results in point-set topology (in my opinion; some > people who style themselves "point-set topologists" look--to the > extent that there are still any of them on the hoof--like straight > out "logicians with an interest in pathology" to most other topologists).
I don't know what Whitehead's problem means, but I have come across similar problems in analysis where the result depends upon what set theory you are using. But after you learn what the result is, you really do feel "ho hum" about it.