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A topological space X is locally compact if every point has a neighborhood which is itself contained in a compact set. Many familiar topological spaces are locally compact, ...

A property that is always fulfilled by the product of topological spaces, if it is fulfilled by each single factor. Examples of productive properties are connectedness, and ...

A map f from a metric space M=(M,d) to a metric space N=(N,rho) is said to be uniformly continuous if for every epsilon>0, there exists a delta>0 such that ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closable if it has a closed extension B:D(B)->H where D(A) subset D(B). Closable operators are ...

A vector basis of a vector space V is defined as a subset v_1,...,v_n of vectors in V that are linearly independent and span V. Consequently, if (v_1,v_2,...,v_n) is a list ...

The squared norm of a four-vector a=(a_0,a_1,a_2,a_3)=a_0+a is given by the dot product a^2=a_mua^mu=(a^0)^2-a·a, (1) where a·a is the usual vector dot product in Euclidean ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...