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Suppose alpha:C_*->D_* and beta:C_*->D_* are two chain homomorphisms. Then a chain homotopy is given by a sequence of maps delta_p:C_p->D_(p-1) such that partial_D ...

While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

A mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b. A mathematical object taken together with ...

Each of the maps of a cochain complex ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->... is known as a coboundary operator.

The first corona of a tile is the set of all tiles that have a common boundary point with that tile (including the original tile itself). The second corona is the set of ...

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

The third-order ordinary differential equation y^(''')+alphayy^('')+beta(1-y^('2))=0.

The flat norm on a current is defined by F(S)=int{Area T+Vol(R):S-T=partialR}, where partialR is the boundary of R.

A disk D in a solid torus V=S^1×D^2 is called meridinal if its boundary is a nontrivial curve in del V (so that it is a meridian). Then a closed subset X subset V is called ...