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Can a space be path-connected and not locally path-connected? (To be clear, "locally path-connected" just means that there is a basis of path-connected of sets.)
My general intuition says no, but my intuition seems to usually be wrong...and this would explain why Hatcher keeps referring to spaces that are both p.c. and l.p.c. in his Algebraic Topology...
My general intuition says no, but my intuition seems to usually be wrong...and this would explain why Hatcher keeps referring to spaces that are both p.c. and l.p.c. in his Algebraic Topology...