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Nowhere Path Connected
Posted:
Jun 23, 2014 8:20 AM


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 connected?



