A topological space 
is pathwise-connected iff for every
two points 
,
there is a continuous function 
from [0,1] to 
such that 
and 
. Roughly speaking, a space 
is pathwise-connected if, for every
two points in 
,
there is a path connecting them. For locally
pathwise-connected spaces (which include most "interesting spaces"
such as manifolds and CW-complexes),
being connected and being pathwise-connected are
equivalent, although there are connected spaces which are not pathwise-connected.
Pathwise-connected spaces are also called 0-connected.
Pathwise-Connected
See also
Connected, Connected Space, Convex, CW-Complex, Locally Pathwise-Connected, Star Convex, Topological SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Pathwise-Connected." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Pathwise-Connected.html