7. Let X be a topological space, let A C X be a subspace, and let i: A → X the inclusion map. Fix a basepoint ao E A, and consider the induced homomorphism on fundamental groups, i*: ₁(A, αo) → π₁ (X, αo). (a) Suppose A is a retract of X. Show that i is injective. (b) Give an example of an inclusion i: A → X where i is not injective.

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A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

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