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A curled ∂ applied to a chain or a region.
Also known as: Boundary operator, Del of a region, Partial symbol in topology
The boundary operator takes a region to its edge, and its defining property is that applying it twice gives nothing — the boundary of a boundary is empty. That one identity is what makes homology possible and is the reason the same curly ∂ appears in both topology and calculus.
Denotes the boundary of a chain or a region.
Contexts: Mathematics
Satisfies ∂∘∂ = 0, the identity that makes homology groups definable at all.
Contexts: Mathematics
Shares its glyph with the partial derivative, and Stokes's theorem is precisely the statement that the two are adjoint.
Contexts: Mathematics
A rounded stroke curling from upper right down and around to the left, forming a closed lower bowl with a hooked top.