For a topological space "X", let "C"b("X"; R) denote the normed vector space of continuous, real-valued, bounded functions "f" : "X" → R equipped with the supremum norm ‖·‖∞. This is an algebra, called the "algebra of scalars", under pointwise multiplication of functions. For a compact space "X", "C"b("X"; R) is the same as "C"("X"; R), the space of all continuous functions "f" : "X" → R. The algebra of scalars is a functional analysis analog of the ring of regular functions in algebraic geometry, there denoted formula_1.