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Date: 27-5-2021
1697
Date: 28-6-2021
1790
Date: 16-7-2021
1913
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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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