Graduate How Does Induced Mapping Function in Algebraic Topology?

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Induced mapping in algebraic topology refers to the functorial nature of maps between topological spaces. Given a continuous function f from space X to space Y, induced maps arise from homology or homotopy groups associated with these spaces. Specifically, if G/N is a group associated with X and G'/N' with Y, the induced map i* takes a homotopy class [a] in π1(X) and sends it to [f(a)] in π1(Y). This demonstrates how properties of spaces can be transferred through continuous functions. Understanding induced mapping is essential for studying the relationships between different topological spaces.
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Given example for what is induced mapping ? In basic level
 
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srgmath2905 said:
Given example for what is induced mapping ? In basic level
Without context this is impossible to answer. The same term is used differently in different contexts.
 
Maybe only commonality is that it's functorial in nature *
*As well as in the wild ;).
Edit: In Algebraic Topology, given f: X-->Y, and groups G/N in X, G'/N' in Y( some (co) homology or Homotopy groups associated to each of X,Y, with N normal in G. N' normal in G), often designated as i* I believe they're of the form:
i*([a])=([f([a])]), from G/N to G'/N'. So a map between cosets.

So, e.g., the homotopy class [a] of ## \pi_1(X)## as above, is sent to the class [f(a)] in ##\pi_1(Y)##.
 
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