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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“The surface of the earth is soft and impressible by the feet of men; and so with the paths which the mind travels. How worn and dusty, then, must be the highways of the world, how deep the ruts of tradition and conformity!”
—Henry David Thoreau (1817–1862)
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