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The closed ball with center x and radius r is defined by B_r(x)={y:|y-x|<=r}.

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 ...

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closed if for any sequence of vectors v_n in D(A) such that v_n->v and Av_n->x as n->infty, it ...

A subset of a topological group which is closed as a subset and also a subgroup.

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 ...

The clove hitch is the hitch illustrated above that is also called the boatman's knot or peg knot.

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.

Let A be a unital C^*-algebra, then an element u in A is called co-isometry if uu^*=1.