A member function of an explicit specialization of a class template is just like a member function of a non-template class. After all, an explicit specialization is a concrete class that does not depend on any template parameter.
If you put its definition in a header file that is included by several translation units, the compiler will produce object code for that function while processing each of those translation units.
Eventually, the linker will complain about multiply defined symbols. The inline
keyword prevents this behavior, just like it does for regular non-template functions or regular member functions of non-template classes.