std::map, custom comparator's design constraints

Question

I have been trying defining a custom comparator for std::map container.

The question is : can I relay on == and != operators or would that break strict weak order ? Am I

Answer 1

This is unacceptable, string weak ordering means that A < B and B < A shall not be true at the same time. std::map relies on this to establish both ordering and equality of the keys