# Example of a space that is connected but not path connected? [duplicate]

Wikipedia says that path-connectedness is a stronger property than connectedness.

My intuition cannot seem to come up with an example of an object that is connected but not path-connected. Are there any examples?

## marked as duplicate by Dietrich Burde, user296602, Forever Mozart, Daniel W. Farlow, John BApr 25 '16 at 0:49

Consider the space $$X=\{(x,\sin x^{-1} ) : x>0\}\cup (\{0\}\times [-1,1])$$ with topology induced by euclidean metric.