I'm reading the paper 'The big fundamental group, big Hawaiian earrings and the big free groups'. The authors state that the class of homotopy equivalences of loops in the space he dubs as the big Hawaiian earrings is not a set. I'm not really certain if what he is saying is true.
I think my question amounts to asking is the class of functions from a set to another set not always a set?
The construction he gives of the big Hawaiian earrings (for ordinal $\omega$) is as the one point compactification of the set of disjoint open intervals with cardinality $\omega$. He then maintains that if $\omega$ has cardinality greater than $\aleph_0$ the resulting class of equivalence classes of homotopic loops is not a group since it's not a set. Is this true? I thought the Hom class of maps between all sets was a set. I'd appreciate any insight, thanks.