The Density Character of the Space Cp (X)

Abstract

The main purpose of this survey is to introduce to the reader the adequate framework and motivation for the recent results obtained relating the density character and the space of the continuous functions, [16]. The interest in this cardinal function has been continuous over the years. We will offer a vision of the process along the time and we will point out different general results. Specially, we are interested in those in which the space of the continuous functions appears as well as those in which duality plays an important role. Of course, precise classes of spaces are considered in each case to apply the results, which will take us forward to expose a parallel development and description of a specific class, in fact it will be the development of a different cardinal function, the number of Nagami, which measures the specific property of the space what makes things work well.