Marcel Brissaud, during the seventies, has been the first to observe the interest of developing mathematical concepts adapted to humanities. Pretopology theory relies on the statement that the axiomatic of mathematical topology is too strong to model the phenomena of social sciences. This axiomatic has to be reconsidered to give birth to a theory that is adapted to data issued from these fields of expertise, better than trying to force data to fit to an existing and inadequate theory.
This book is the first English revised version of a first book, published in French, which is planned to be the first of a series dedicated to the whole set of results obtained in Pretopology: continuity, connectedness, associated metric... any applications of Pretopology were conducted in various fields: economy with the structural analysis of a economy, game theory with the study of the dynamics of coalitions in cooperative games, sociology with analysis of social networks, data analysis with the construction of clustering algorithms, pattern recognition with digital image analysis as in mathematical morphology, etc. Purely mathematical work in Pretopology has enabled the building of processing algorithms that have been put in a software library, PRETOPOLIB, allowing researchers to implement a pretopological approach in their work.