I have an object that contains a set of other objects

public class Item
{
}

public class ItemCollection : HashedSet<Item>
{
}

public class Part
{

ItemCollection itemCollection;
}

How can I specify this?

If I change :
ItemCollection itemCollection;
to
ISet<Item> itemCollection;

it works fine, but I don't want that. I want to be type safe and use the correct class.

Any ideas?

I don't see any caveats from you construction. In my opinion it is always the best approach to use interface if possible. Using the ISet<...> is safe with respect to any aspect, isn't it?

Please describe what exactly your goal is?

If I want to search my collection for a specific item (say by name) I would like to create a function in my collection class:

class ItemCollection : HashedSet<Item>
{
Item SearchByName(string name)
{
foreach(Item i in this)
if(i.Name == name)
return i;
return null;
}
}

I can't do this is all I have is ISet<Item>.

What is the behavior when you use your collection? Did you get any exception?

Again, I think that such algorithms should rather be in the DAO layer. The domain objects should be as transparent as possible. Introducing such functionality you inject a logic to the data objects. Later when you want to have different behavior (just in one case where other applications should remain original) you will have to change the code.