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ABSTRACT
Pretopology is a mathematical field cousin of General Topology dealing with pre-topological spaces, i.e. of sets equipped with more general structures than topologies and defined via pre-closure operators, including topological closure operators as a special case. It allows compensating for a too big restriction of the axiomatic of topological spaces, and its application fields are many and varied, in both formal, natural and human sciences and engineering. This article presents its concepts and basic notions following the canvas of gradual exposure of General Topology, in order to allow the reader to understand the similarities and differences. 36 detailed examples of application issues are exposed.
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Jean-Charles PINOLI: Professor - École Nationale Supérieure des Mines de Saint-Étienne, Saint-Étienne, France - To Dr Séverine Rivolier for her scientific interest.
INTRODUCTION
Pretopology is a branch of mathematics, a cousin of general topology, which deals with pretopological spaces, i.e. sets with structures more general than topologies and defined via preclosure operators, of which classical topological closure operators are a special case. It makes up for the over-restriction of the axiomatics of topological spaces, and its fields of application are many and varied, in the formal, natural and human sciences, as well as in engineering. This article presents the basic concepts and notions, following the progressive exposition of general topology, to enable the reader to understand the similarities and differences. Thirty-six detailed application examples are presented.
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KEYWORDS
continuity | pretopological spaces | neighborhoods | preclosure operators
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