Path-connected space

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This is a variation of connectedness. View other variations of connectedness

Definition

Symbol-free definition

A topological space is said to be path-connected' or arc-wise connected if given any two points on the topological space, there is a path (or an arc) starting at one point and ending at the other.

Definition with symbols

A topological space X is said to be path-connected if for any two points a,b \in X there is a continuous map \gamma:[0,1] \to X such that \gamma(0) = a and \gamma(1) = b.

Relation with other properties

Weaker properties