Proceedings on non commutative geometry

This book deals with generalizations of topology and in particular metricity. Given that those subjects arise out of Boolean logic, we diligently present this material first. Later on, quantal logic is studied as well as generalizations thereof. This leads to the study of simple quantum geometries such as the non commutative simplex. Furthermore, generalizations of classical geometry are presented leading to the notion of a quantal metric space attached to a classical one.