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

A metric space X is said to be locally path-connected if for every x ∈ X and every open neighborhood V of x in X, there exists a path-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 ⇒ local path-connectedness.

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Expert Solution

Colby Messinger answered 1 year ago

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