![[Image: A-The-classical-Borsuk-Ulam-theorem-for-...of-S-n.png]](https://www.researchgate.net/profile/Arturo-Tozzi/publication/285538189/figure/fig1/AS:302197880442893@1449060997552/A-The-classical-Borsuk-Ulam-theorem-for-different-values-of-S-n.png)
Borsuk–Ulam theorem
Summary
The Borsuk–Ulam theorem is a fundamental result in algebraic topology stating that any continuous function from an $n$-sphere into $n$-dimensional Euclidean space must map at least one pair of diametrically opposite (antipodal) points to the exact same point.
Informally, this means that if you continuously map a spherical surface into a flat space of one lower dimension, there will always be a pair of opposite points that end up at the same location—a classic meteorological consequence of which is that at any given moment, there are always two opposite points on Earth's surface that share the exact same temperature and barometric pressure.
ARTICLE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘