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  3. a metric space x is said to be locally path-connec

A metric space X is said to be locally path-connected if for every x ? X...

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Advance Math

A metric space X is said to be locally path-connected if forevery x ? X and every open neighborhood V of x in X, there exists apath-connected open neighborhood U of x in X with x ? U ? V.

(a) Show that connectedness + local path-connectedness ?path-connectedness

(b) Determine whether path-connectedness ? localpath-connectedness.

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