A Classification of Elements of Function Space F(R,R)

In this paper, we present a constructive description of the function space all real-valued functions on R(F(R,R)) by presenting partition it into 28 distinct blocks and closed-form formula for representative each them. Each block contains elements that share common features in terms cardinality their sets continuity differentiability. Alongside classification, introduce concept Connection, which reveals special relationship structure between well-known representatives four blocks: Cantor function, Dirichlet Thomae Weierstrass function. Despite significance field, several perspectives remain unexplored.