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Date: 24-6-2021
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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.
REFERENCES:
Joshi, K. D. Introduction to General Topology. New Delhi, India: Wiley, p. 151, 1983.
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