  The so-called $\delta'$-interaction as a particular example in Kurasov's
distribution theory developed on the space of discontinuous (at the point of
singularity) test functions, is identified with the diagonal transmission
matrix, {\em continuously} depending on the strength of this interaction. On
the other hand, in several recent publications, the $\delta'$-potential has
been shown to be transparent at some {\em discrete} values of the strength
constant and opaque beyond these values. This discrepancy is resolved here on
the simple physical example, namely the heterostructure consisting of two
extremely thin layers separated by infinitesimal distance. In the three-scale
squeezing limit as the thickness of the layers and the distance between them
simultaneously tend to zero, a whole variety of single-point interactions is
realized. The key point is the generalization of the $\delta'$-interaction to
the family for which the resonance sets appear in the form of a countable
number of continuous two-dimensional curves. In this way, the connection
between Kurasov's $\delta'$-interaction and the resonant-tunneling point
interactions is derived and the splitting of the resonance sets for tunneling
pla ys a crucial role.
