path-connected

Adjective

Meaning

path-connected (not comparable)

(of a topological space) Such that every pair of points in the space comprises the boundary of some path mapped to the space continuously.

Source: en.wiktionary.org

Examples

If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 ). Source: Internet

Path connectedness This subspace of R² is path-connected, because a path can be drawn between any two points in the space. Source: Internet

A locally path-connected space is connected if and only if it is path-connected. Source: Internet

Every path-connected space is connected. Source: Internet

Every ultra-connected space is path-connected. Source: Internet

Geometric interpretation Conjugacy classes in the fundamental group of a path-connected topological space can be thought of as equivalence classes of free loops under free homotopy. Source: Internet

Close letter words and terms

path traversal path- path-breaker path-finder Pathak Pathan