Sentence examples for spaces and hence from inspiring English sources

High moisture content reduces air spaces and hence compost becomes clumpy.

This fact actually characterizes Hilbert spaces and hence, it is not available in more general Banach spaces.

The proofs are almost the same as in [19] for the case of b-metric spaces and hence we omit them.

Very recently it has been shown in [4] that the so-called E-convex Banach spaces, and hence the uniformly nonsquare ones, have the PSz property.

It is more difficult to measure these parameters in occupied spaces and hence being able to predict occupied values of these acoustical parameters from unoccupied measurements is a great asset to achieving acoustically successful classrooms.

Since (mathcal{A}) is a symmetric densely defined operator, then it is sufficient to show that the deficiency spaces are the null spaces and hence (mathcal{A}=mathcal{A}^).

It is well known that the spaces c and (l_{infty}) endowed with the norm ({Vert cdot Vert } _{infty}) are BK-spaces, and hence the space (f(bar{N})) endowed with the norm ({Vert cdot Vert } _{infty}) is also a BK-space.

Then ((X, Gamma)) is a G-convex space and hence an abstract convex space.

This increases the size of the state space and hence the computational complexity.

For example, the set of fuzzy real numbers is not a vector space and hence it cannot be Banach space.

Then, (K, d) is a CAT 0) space and hence it is a CAT kappa)) space for all (kappa >0).