In mathematical representation theory, two representations of a group on topological vector spaces are called Naimark equivalent (named after Mark Naimark) if there is a closed bijective linear map between dense subspaces preserving the group action.
An open bijective linear map will satisfy the requirements of Naimark equivalence in no circumstances
The bijective linear map must be closed so being open will indeed never satisfy the requirements. The placement of the qualifiers in the sentence probably confused the system