Sentence examples for space over mathcal{ from inspiring English sources

Let E be a real Banach space over (mathcal{R}).

For simplicity, we always assume that (mathcal{A}) is a real Banach algebra and ((X,d)) is a complete partial ordering cone metric space over (mathcal{A}) with the partial ordering '⩽' induced by φ, where (varphi: Xrightarrowmathcal{A}) is continuous.

In the rest of this section, we always assume that (mathcal{A}) is a real Banach algebra and ((X,d)) is a complete partial ordering cone metric space over (mathcal{A}) with the partial ordering '⩽' induced by φ, where (varphi: Xrightarrowmathcal{A}) is continuous, P is a solid cone of (mathcal{A}) which gives the partial ordering '⪯' in (mathcal{A}).

Let ((E,Vert cdot Vert )) be a normed space over a field (mathcal{K}) (either (mathbb{R} ) or (mathbb{C} )), (I=[a,b]) be a closed interval in (mathbb{R} ) and (cin I).

Let and be seminormed spaces over and.

Meanwhile, ((X, d)) is called a partial ordering cone metric space over the Banach algebra (mathcal{A}).

Let ((X,d)) be a partial ordering cone metric space over the Banach algebra (mathcal{A}).

end{aligned} Then ((X,d)) is a complete cone 2-metric space over the Banach algebra (mathcal{A}).

Let ((X,d)) be a complete cone 2-metric space over the Banach algebra (mathcal{A}) and P be the underlying solid cone.

Then d is called a cone metric on X and ((X, d)) is called a cone metric space over the Banach algebra (mathcal{A}).

Let ((X,d)) be a complete cone 2-metric space over the Banach algebra (mathcal{A}) and let P be the underlying solid cone in (mathcal {A}).