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wofsy
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Can you show me a metric on the 2 dimensional disc so wild that no open subset can be embedded in R^3?
zhentil said:Embedded isometrically? Otherwise, it's false.
The "Wild metric" on the 2 disc refers to a mathematical concept that measures the distance between points on a 2-dimensional disc. It is called "wild" because it is a non-standard metric, meaning it does not follow the usual rules of distance measurement.
The "Wild metric" is calculated using a formula that takes into account the geometric properties of the 2 disc. Unlike the traditional Euclidean metric, the "Wild metric" takes into consideration the curvature and boundaries of the disc in its calculation.
Studying the "Wild metric" on the 2 disc can provide insights into non-Euclidean geometry and help us understand how distance is measured in curved spaces. It also has applications in fields such as physics, computer science, and topology.
The "Wild metric" differs from the traditional Euclidean metric in that it takes into account the curvature and boundaries of the 2 disc, while the Euclidean metric assumes a flat, infinite space. This results in different distance measurements between points on the disc.
Yes, the "Wild metric" can be extended to higher dimensions, such as the 3-dimensional sphere. However, the calculations become more complex as the number of dimensions increases. Therefore, the "Wild metric" is most commonly studied in 2 dimensions.