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.
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“All forms of beauty, like all possible phenomena, contain an element of the eternal and an element of the transitory—of the absolute and of the particular. Absolute and eternal beauty does not exist, or rather it is only an abstraction creamed from the general surface of different beauties. The particular element in each manifestation comes from the emotions: and just as we have our own particular emotions, so we have our own beauty.”
—Charles Baudelaire (1821–1867)
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