The subset
of the Euclidean plane formed by the union of
the *x*-axis, the line
segment with interval
of the *y*-axis, and the sequence of segments with
endpoints
and for all positive integers .

With respect to the relative topology is pathwise-connected. It is therefore connected, but not locally pathwise-connected at any point of the open interval since each open disk centered at point one of these points intersects in a union of parallel segments, forming a disconnected set.