Topological classification of Cp(X) function spaces

In this study, it is considered topological side of Cp-theory. It is researched that topological and linear topological properties of Cp(X).X and Y are Tychonoff spaces such that Cp(X) and Cp(Y) are linear homeomorphic. It was searched that for which properties of X and Y, X and Y are homeomorphic.Topologies were formed over function spaces.And linear and continuous linear mappings were formed between these spaces. It was given a classification of spaces Cp[(1,a)] of continuous real valued functions on ordinals. It was searched that which property is necessary on a topological space to be l-equivalent to the n-dimensional cube.Key words: Tychonoff space, function space, linear homeomorphic, Cp -theory, ordinal, l-equivalent