The projective plane is a non-orientable surface which is not representable (can be merged) in our usual three-dimensional space. After returning to a few definitions and properties of the projective plane, I will give some examples of the uses that Jacques Lacan of this topological object. These include representations involving the subject of the unconscious. However what is presented is not a formal mathematical work and includes trivialisations which can go against mathematicians. Jacques B.Siboni
