On a Unified Analysis in the language of preordered sets

Abstract: We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of all mentioned notions follow from one single theorem. A generalisation of Definition 1 contains basic ideas of other theories such as topology, group and measure theory.