Sentence examples for path connectedness from inspiring English sources

We assume that the reader has had a first course in point-set topology, but we do discuss quotient spaces, path connectedness, and function spaces.

Topological properties of solution sets of vector optimization have been extensively studied with central themes being compactness, (path) connectedness, contractibility, retractability, etc. (see, e.g., the works by Benoist [47] and Huy [48] and his group for a number of non-convex vector optimization settings).

Note also that path-connectedness implies non-simplicity.

One variant drops the agenda property of path-connectedness and strengthens independence to systematicity.

A final variant drops both path-connectedness and pair-negatability while imposing both systematicity and monotonicity (ibid).

See also the remark on the relationship between path-connectedness and non-simplicity at the end of this subsection.

Zhong et al. [32] have studied the connectedness and path-connectedness of solutions set for symmetric VEPs.

Therefore, non-simplicity need not be listed among the theorem's conditions, though it is needed in the variants dropping path-connectedness.

However, as seen above, the orthants composing the tree space have a rich adjacency structure, which guarantees at least the path-connectedness of the space: any two phylogenetic trees can be connected by at least one path that remains in this space, although this path might not be a straight line as in R + 2 n − 1 whenever the topologies differ.

That Compact Flash slot is the Axim's path to connectedness.

Many of us have moved on to other smartphones — iPhones and Android devices, mostly — but the BlackBerry, as the object that started us down this path of constant connectedness, holds a special place in the collective heart of the American workforce.