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A Greek chi of a space, a single whole number invariant.
Also known as: Euler characteristic, Chi of a space, Euler number
The Euler characteristic is vertices minus edges plus faces, and it is the same number for every way of cutting a given surface up. It is 2 for any sphere and 0 for any torus, which is the cleanest example of a topological invariant a reader can check by counting.
Denotes the Euler characteristic: an integer invariant computed as the alternating sum of cell counts.
Contexts: Mathematics
Is 2 for every surface homeomorphic to a sphere and 0 for every torus, independently of how it is subdivided.
Contexts: Mathematics
Generalises to the alternating sum of Betti numbers, which is why it is defined for spaces that cannot be drawn.
Contexts: Mathematics
A Greek lowercase chi — two crossing diagonal strokes, one curved — followed by a bracketed space name.