Additionally, Superspace is a synonym for "Super Vector Space" which uses Vector space and uses the variable K.
In Vector Space (Which Superspace and Super Vector Space uses) Infinite Dimensions can occur naturally:
"Vector spaces are the subject of
linear algebra and are well characterized by their
dimension, which, roughly speaking, specifies the number of independent directions in the space. Infinite-dimensional vector spaces arise naturally in
mathematical analysis, as
function spaces, whose vectors are
functions. These vector spaces are generally endowed with additional structure, which may be a
topology, allowing the consideration of issues of proximity and
continuity. Among these topologies, those that are defined by a
norm or
inner product are more commonly used, as having a notion of
distance between two vectors. This is particularly the case of
Banach spaces and
Hilbert spaces, which are fundamental in mathematical analysis."
to further clairify:
"Vector spaces, including infinite-dimensional ones, then became a firmly established notion, and many mathematical branches started making use of this concept."
