A new class of fuzzy spaces with classical limit

We present a new type of matrix regularization, which is based on matrix-valued functions defined on a cylinder. If non-commutative coordinates of a fuzzy space are defined by a regularization of such functions, we show that a classical limit for the fuzzy spaces exists, when the matrix-valued functions nearly commute. In this case, the classical limit of the fuzzy space is a manifold, which is composed of coordinate patches that are defined by the diagonal entries of the diagonalized matrix-valued functions. As applications, an interpolation for direct sums of fuzzy spaces is described and a fuzzy string vertex with classical limit, i.e. a surface interconnecting three circles, is constructed.