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Topic: Nowhere Path Connected
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William Elliot

Posts: 2,637
Registered: 1/8/12
Nowhere Path Connected
Posted: Jun 23, 2014 8:20 AM
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A space S is nowhere path connected when every path is a constant map.
The cofinite integers is a connected, nowhere path connected space.

Roy's lattice space and the relative prime integer topology (space #60
in Steen's "Counterexamples in Topology") are countable, connected,
Hausdorff spaces;  thus nowhere path connected.

Is there any multipoint connected metric space that's nowhere path

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