ABSTRACT
Metric spaces were introduced and studied by the French mathematician, Maurice Renk Frkchet (in his doctoral dissertation published in 1906), and developed later by German Felix Hausdorff (in his book Grundziige der Mengenlehre of 1914). It was apparent that to the end of the nineteenth century the mathematical world (partly inspired by Cantor's fundamental work in set theory) was eager to structure more general sets than conventional Rn. On the other hand, the needs of complex analysis and the rash development of differential equations speeded up this process. Typical examples are uniform convergence in function spaces, approximation of continuous functions by polynomials and the Riemann mapping theorem. After 1920, the theory of metric spaces, especially, fundamental work on normed spaces and their applications to functional analysis, was further developed by Pole Stefan Banach and his school. Paying a tribute to their achievements and of their other fellow countrymen followers, an important subclass of metric spaces was named "Polish." A series of studies of metric spaces were further undertaken in the late 1920s by the Russian school of analysis. At this time, metric spaces have become generalized to topological spaces.
