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  "body": "\n## Example\n\nLet $\\sim$ be the equivalence relation on the square $[0, 1] \\times [0, 1]$ generated by $(0, y) \\sim (1, 1 - y)$ for all $y \\in [0, 1]$.\nThe quotient space $[0, 1]^2 / {\\sim}$, with the [[quotient topology|0V8046R0P9]], is the Möbius strip.\n\n## Remarks\n\nThe gluing has a half-twist: the bottom of the left edge is glued to the top of the right edge.\nThe Möbius strip is a non-orientable surface. Its boundary is one circle, not two.\nWithout the twist, the gluing $(0, y) \\sim (1, y)$ gives a cylinder, which is not homeomorphic to the Möbius strip.\n\n## Explanations\n\n### L1 human\n\nTake a strip of paper, give one end a half-turn, and glue the two ends together.\nThe result has only one side: an ant can walk to every point of the strip without crossing an edge.\n",
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