Sentence examples for spaces is required from inspiring English sources

Now, for non-contraction mappings, complete metric spaces are in general not sufficient to guarantee the existence or uniqueness fixed points; in this regard, usually, compactness and/or convexity of subsets of normed linear spaces is required.

More importantly, systematic investigation of generated knowledge in both the chemical and biological knowledge spaces is required, especially in the scenarios of identifying both new targets and their potential ligands, discovering potential biomarkers for complex diseases, understanding the mechanism of interactions, and discovering new regulatory mechanism etc. [3 8].

It means that more computation efforts and memory spaces are required for vector-sensor array signal processing.

In term of the BS, N c independent spaces are required to receive N c target flows.

Locating new urban developments in vulnerable areas increases the exposure to uncertainties, hence this is not recommended as these spaces are required for creating the space to implement sustainability principles.

He insisted that two spaces were required.

For example, instead of considering all linear maps (also called functionals), maps between topological vector spaces are required to be continuous.

Each hen in a cage-free environment needs a minimum range of 1 to 1.5 square feet of floor space to itself, and nesting and perching spaces are required.

Affixed to a wall near the door leading outside was a plaque enumerating exactly how many trees, seats, chairs, and tables the space is required to contain — requirements that Trump has sometimes ignored.

For those 3 to 5 years old, 35 square feet of space is required per child.

How much minimum space is required to keep this pet, indoors or outdoors?