  We generalize the notion of Gelfand triples (also called Banach-Gelfand
triples or rigged Hilbert spaces) by dropping the necessity of a continuous
embedding. This means in our setting we lack of a chain inclusion. We replace
the continuous embedding by a closed embedding of a dense subspace. This new
notion will be called quasi Gelfand triple. These triples appear naturally,
when we regard the boundary spaces of spatially multidimensional differential
operators, e.g., the Maxwell operator. We will show that there is a smallest
space where we can continuously embed the entire triple. Moreover, we will show
density results for intersections of members of the quasi Gelfand triple.
Finally, we show that every quasi Gelfand triple can be decomposed into two
"ordinary" Gelfand triples.
