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Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

A spectrum sequence is a sequence formed by successive multiples of a real number a rounded down to the nearest integer s_n=|_na_|. If a is irrational, the spectrum is called ...

A function, continuous in a finite closed interval, can be approximated with a preassigned accuracy by polynomials. A function of a real variable which is continuous and has ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

A space curve consisting of a spiral wound around a helix. It has parametric equations x = [R+acos(omegat)]cost (1) y = [R+acos(omegat)]sint (2) z = ht+asin(omegat). (3)

A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk (2000) present ...

A topological space M satisfying some separability (i.e., it is a T2-space) and countability (i.e., it is a paracompact space) conditions such that every point p in M has a ...

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

A basepoint is the beginning and ending point of a loop. The fundamental group of a topological space is always with respect to a particular choice of basepoint.