Sentence examples for be the closed unit from inspiring English sources

Let B be the closed unit ball of (ell_{2}).

Let B̅ be the closed unit ball in ({mathbb{R}}^{2}) in the (ell^{p} -metric.

Let be a CNS and let be the closed unit interval.

Let be the closed unit disc in with polar coordinates and the usual Euclidean norm.

Let G be the closed unit ball of some norm on Cn, and let A(G) be the closure of the polynomials in the sup norm.

Define to be the closed unit square with the topology defined by taking as a neighborhood basis of each point off the diagonal the intersection of with open vertical line segments centered at (e.g., ).g.

Therefore, since (mathcal {D} K_j ) rightarrow 0), we conclude that (P K =P(B)) and thus that K is the closed unit ball centered at the origin.

Without loss of generality, we assume that the compact set K in the main theorem is the closed unit cylinder (overline{Q}_{1}), and, moreover, that (overline{Q}_{2}subsetOmega_{T}).

A topological space X is said to be n-connected for n ≥ 0 if every continuous map f : S k → X for k ≤ n has a continuous extension over B k + 1, where S k is the unit sphere and B k + 1 is the closed unit ball in R k + 1.

As a consequence of the approach used, some results about sections of unit balls are also derived, namely VolH H ∩ BpM) ⩽ Volk(Bpk) for 0 < p ⩽ 2, where BpM, Bpk are the closed unit balls centred at zero of the spaces lpM and lpk, respectively, H is a k-dimensional subspace of lpM, and Volk, VolH denote Lebesgue measures in Rk and H, respectively.

This is a more general problem than the one-variable version of finding or characterizing the largest biconvex function (zeta:overline {B}timesoverline{B}rightarrowmathbb{R}) such that (zeta x,y le |x+y|_{p}) whenever (|x|_{p}=|y|_{p}=1), where B̅ is the closed unit ball in ({mathbb{R}}^{2}) in the (ell^{p} -metric, obtainell^{p} -metriciable y is fixed.