A Klein surface is, as for Riemann surfaces, a surface with an atlas allowing the transition functions to be composed using complex conjugation. One can obtain the so called dianalytic structure of the space.
Read more about this topic: Klein Bottle
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“There’s something tragic in the fate of almost every person—it’s just that the tragic is often concealed from a person by the banal surface of life.... A woman will complain of indigestion and not even know that what she means is that her whole life has been shattered.”
—Ivan Sergeevich Turgenev (1818–1883)