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Joined 1 year ago
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Cake day: December 8th, 2024

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  • I am not a topologist, but I can try…

    A space (shape) is contractible if you can “contract” (shrink) it to a point without cutting, pinching or punching through holes. For example, a mattress is contractible, since you can shrink it to the center - each point can follow the line to the center, continuously. Meanwhile, a doughnut, a circle or a hollow sphere are not contractible, you can never remove the inner “hole” to shrink to a point without cutting.

    In general, any dimensional sphere is not contractible… Until it isn’t - infinite dimensional sphere is . Somehow, it loses the “hollow space” inside.