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A compact manifold without boundary.

A map f between topological spaces that maps closed sets to closed sets. If f is bijective, then f is closed <==>f is open <==>f^(-1) is continuous, where f^(-1) denotes the ...

The set closure St^_v of a star Stv at a vertex v of a simplicial complex K.

Let p be a non-wandering point of a diffeomorphism S:M->M of a compact manifold. The closing lemma concerns if S can be arbitrarily well approximated with derivatives of ...

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->..., the module B^i of i-coboundaries is the image of d^(i-1). It is a submodule of C^i and is ...

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 inverse curve of the cochleoid r=(sintheta)/theta (1) with inversion center at the origin and inversion radius k is the quadratrix of Hippias. x = ktcottheta (2) y = kt. ...

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->... the module Z^i of i-cocycles Z^i is the kernel of d^i, which is a submodule of C^i.

Code 177 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.