Set and .equals() semantics

I must be missing something involving the lack of a 'get' method for Sets.

Briefly, my app maintains a Collection of unique Foo() objects derived 
by reading and parsing an InputStream. The objects being stored have an
equals() method which compares the im****tant attributes. So far, very 
basic and simple.

It seemed to me the obvious type for holding this collection of
unique objects was a Set, so that's how I did it. The input-reading 
method grabs a line of input, parses it, and creates a "Foo foo = new 
Foo()". If an equivalent instance (as determined by equals()) is already 
present in the set, I want to let the new one go out of scope. If not 
already present, I want to add it. Still, simple and basic.

Here's where things go sideways: I also need to store a reference to 
'foo' in another new object. If this is the first time I've seen it, 
everything is fine because I already have the reference and can add it 
to both places, e.g.

	fooSet.add(foo);
	bar.addFoo(foo);

But if it was already present in the Set, I'm left holding a reference 
to the "tem****ary" copy which is about to go out of scope. I know 
there's an identical copy already in the Set but there's no way to 
retrieve it in order to add it to the Bar object.

I've switched over to using

	Map<Foo, Foo>

which can both look up and retrieve a reference. But I hope I'm 
misunderstanding something which would allow me to use the more natural 
Set design.

Thanks,
RM