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On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

Irreducible orientable compact 3-manifolds have a canonical (up to isotopy) minimal collection of disjointly embedded incompressible tori such that each component of the ...

A simple root of a Lie algebra is a positive root that is not the sum of two positive roots.

One of the Eilenberg-Steenrod axioms. It states that, for every pair (X,A), there is a natural long exact sequence ...->H_n(A)->H_n(X)->H_n(X,A)->H_(n-1)(A)->..., where the ...

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

The two-dimensional space consisting of the set of triples {(a,b,c):a,b,c in K, not all zero}, where triples which are scalar multiples of each other are identified.

Let R be a ring, let A be a subring, and let B be an ideal of R. Then A+B={a+b:a in A,b in B} is a subring of R, A intersection B is an ideal of A and (A+B)/B=A/(A ...

A sigma-compact topological space is a topological space that is the union of countably many compact subsets.

A family composed of countably many locally finite families.