Path-connected space

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 or arc-wise 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 $$\gamma(1) = b$$.

Stronger properties

 * Simply connected space
 * Contractible space

Weaker properties

 * Connected space:

Textbook references

 * , Page 155 (formal definition)
 * , Page 52 (formal definition): introduced under name arcwise connected space
 * , Page 25 (formal definition)