Isometries between Indistinguishability Operators
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If we look at the definition and properties of T -indistinguishability operators, we can see that they show very metric behaviour. This is because they are a special case of a more general structure called Generalized metric spaces. Generalized metric spaces were introduced by E. Trillas (,) as a general framework for dealing with different concepts of distance appearing in places such as metric spaces, probabilistic metric spaces, lattice metrics, etc. The idea is to valuate the map by defining the ‘distance’ between objects in an ordered semigroup, such that they are defined as follows:
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