Hello Math experts, i need some help
let be a topological space.
Let and let be a retraction.
Given , show that is surjective
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In general, if and if are functions, and if , then g is injective, and f is surjective.
In your scenario, let be the inclusion. Then , and by going to the induced maps on fundamental groups, we get
so the map induced by r is surjective.
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