# What does $H=\{h\mid h:X\rightarrow Y\}$ mean?

I have never used this notation before. I did some digging, but closest thing I could find is: What does the function f: x ↦ y mean?

Can anybody explain this notation?

It means that $$H$$ is the set of all functions from the set $$X$$ to the set $$Y$$.
Read literally, we could say the statement as "$$H$$ is the set of all functions $$h$$ such that $$h$$ has domain $$X$$ and codomain $$Y$$."
(Anecdotally, $$X,Y$$ need not necessarily be sets - could be rings, vector spaces, groups, whatever: the context in which this appears should make it clear. I imagine if this is your first time coming across it, it's probably about sets though.)
$$H$$ is the set of all functions with domain $$X$$ and codomain $$Y$$.
Another way to write it would be $$H=Y^X$$. It's the set of all functions from $$X$$ to $$Y$$.