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  3. (connected spaces) (a) let <x, d> be a metri

(Connected Spaces) (a) Let <X, d> be a metric space and E ? X. Show that...

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Advance Math

(Connected Spaces)
(a) Let be a metric space and E ? X. Show that E isconnected iff for all p, q ? E, there is a connected A ? E with p,q ? E.
b) Prove that every line segment between two points in R^k
is connected, that is Ep,q = {tp + (1 ? t)q |
t ? [0, 1]} for any p not equal to q in R^k.
C). Prove that every convex subset of R^k is connected.

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