Sentence examples for concepts of continuity from inspiring English sources

During the 18th century calculus became increasingly algebraic, as mathematicians most notably the Swiss Leonhard Euler and the Italian French Joseph-Louis Lagrange began to generalize the concepts of continuity and limits from geometric curves and bodies to more abstract algebraic functions and began to extend these ideas to complex numbers.

Using the concepts of continuity, mixed monotone property and coupled fixed point, Choudhary and Maity [31] introduced the following theorem.

For a comprehensive account of the evolution of the concepts of continuity and the infinitesimal, see Bell (2005), on which the present article is based.

Similarly to ordinary analysis, the concepts of continuity and of the Lipschitz condition for mapping on vector metric spaces have been introduced and have been applied for proving the existence of fixed points (see [2 4]).

We need to avoid narrow, service-based concepts of continuity if we are to understand its impact on health outcomes.

This research was part of a wider programme commissioned by NIHR Service and Delivery Organisation to explore concepts of continuity of care in chronic disease.

Notice that the concept of α-completeness of metric spaces is weaker than the concept of completeness and the concept of an α-continuous multivalued mapping is weaker than the concept of continuity in metric spaces.

There was the whole concept of continuity.

Next, we propose another concept of continuity.

The concept of continuity by deploying new nodes in the area has been studied under multiphase wireless sensor network topic in the literature.

Either one takes the option to simply drop the notion of dimension on the basis of the argument that the concept of dimension presupposes a concept of continuity and topology and hence has no finitist meaning.