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In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted ...

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.